inclusionAI/Ring-lite-rl-data huggingface dataset:
Thirty nine nonzero numbers are written in a row. The sum of any two neighbouring numbers is positive, while the sum of all the numbers is negative. Is the product of all these numbers negative or positive?    (4 points)
                                                                                                                           
                                                       Boris Frenkin
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{positive}
Find the number of distinct roots of the equation $\overline{z} + z^2 = i(\overline{z} - z^2)$ in the set of complex numbers, where $\overline{z}$ represents the complex conjugate of $z$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
Three cards are dealt at random from a standard deck of 52 cards. What is the probability that the first card is an Ace, the second card is a diamond, and the third card is a Jack?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{650}}
考虑 \ln(1+x+x^2+x^3) 在 x=0 处的泰勒展开，设 x^{2024} 项的系数为 a. 求 [|a|^{-1}].
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{674}
If 125% of j is equal to 25% of k, some percentage of k is equal to 50% of l, and 175% of l is equal to 75% of m, then 20% of m is equal to 700% of 100% of j. What is the percentage of k that is equal to 50% of l?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{150\%}
Tom decides to lease a car. He drives 50 miles on Monday, Wednesday, and Friday, and Sunday for the rest of the days he drives 100 miles. He has to pay $.1 per mile he drives. He also has to pay a certain weekly fee. He has to pay $7800 in a year. How much is the weekly fee he has to pay?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\$95}
In the context of Number Theory, determine the explicit value of the sum $\sum_{n=1}^{9999}\frac{1}{(n+1)^{\frac{1}{4}}}$ using a method other than Abel's formula.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1332}
What is the maximum number of white and black pieces that can be placed on a chessboard so that in each row and each column the number of white pieces is exactly twice the number of black pieces?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{48}
一个盒中有 9 个正品和 3 个废品, 每次取一个产品, 取出后不再放回。则在取出 2个正品前已取出 3 个废品的概率为 $\qquad$.原始的答案是\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{56}
设 $\mathbf{M}=\{1,2,3, \cdots, 1995\}, \mathbf{A}$ 是 $\mathbf{M}$ 的子集且满足条件: 当 $x \in \mathbf{A}$ 时, $15 x \notin \mathbf{A}$, 则 $\mathbf{A}$ 中元素的个数最多是
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1870}
定义在$R$上的函数$f\left( x \right)$满足$f\left( 0 \right)=0$，$f\left( x \right)+f\left( 1-x \right)=1$，$f\left( \frac{x}{5} \right)=\frac{1}{2}f\left( x \right)$，且当$0\le {{x}_{1}}<{{x2}}\le 1$时，$f\left( {{x}_{1}} \right)\le f\left( {{x2}} \right)$，则$f\left( \frac{1}{2019} \right)=$_______．
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$\frac{1}{32}$}
A merchant has two types of goods. He marks up the first type of goods by 45% and then offers a discount of 15% on the marked price. For the second type of goods, he marks them up by 75% and then offers a discount of 30% on the marked price. If the merchant sells equal amounts of both types of goods, what is the overall percentage profit for the merchant after the discounts?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{22.88\%}
5. Let's call the arrangement of $N$ grasshoppers on a line at various points of it $k$-successful if, after making the necessary number of moves according to the rules of leapfrog, the grasshoppers can achieve that the sum of pairwise distances between them decreases by at least $k$ times. For which $N \geqslant 2$ does there exist an arrangement that is $k$-successful for all natural $k$? (In leapfrog, on a move, one of the grasshoppers jumps to the point symmetric to it relative to another grasshopper.)

M. Svyatlovsky
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{N\geqslant3}
Let \[ f(N, r) \equiv \prod_{p \leq N} (1 + p^{-r}) \quad 0 < r < 1 \] where $p$ runs through all the primes less than or equal to $N$. What is the order of magnitude of $f(N, r)$ as $N \to \infty$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\exp\left[\frac{N^{1-r}}{(1-r)\ln(N)}\right]}
Susie babysits every day for 3 hours a day at the rate of $10 per hour. She spent 3/10 of the money she earned from last week to buy a make-up set. She then spent 2/5 of her money on her skincare products. How much is left from her earnings last week, in dollars?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$88.2}
Determine the number that does not divide the expression $n^{2225} - n^{2005}$ for every integer value of $n$. Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
Evaluate the integral $$\iiint_E\sqrt{3x^2+3z^2}\,dV$$ where the solid $E$ is bounded by the paraboloid $y=2x^2+2z^2$ and the plane $y=8$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\(\frac{256\sqrt{3}\pi}{15}\)}
Arrange six positive integers \(a, b, c, d, e, f\) in a sequence in alphabetical order such that \(a=1\). If any positive integer is greater than 1, then the number that is one less than this integer must appear to its left. For example, \(1,1,2,1,3,2\) meets the requirement; \(1,2,3,1,4,1\) meets the requirement; \(1,2,2,4,3,2\) does not meet the requirement. Find the number of different sequences that meet the requirement.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{203}
A school is adding 25 rows of seats to the auditorium. The first 10 rows will have 20 seats each, the next 10 rows will have 15 seats each, and the remaining 5 rows will have 10 seats each. Seat prices vary by section: each seat in the first 10 rows costs $60, each seat in the next 10 rows costs $50, and each seat in the remaining rows costs $40. A parent, being a seat manufacturer, offers a tiered discount based on seat types: 

- For the $60 seats: 12% discount for each group of 20 seats purchased.
- For the $50 seats: 10% discount for each group of 15 seats purchased, and an extra 3% discount if 30 or more seats are purchased.
- For the $40 seats: 8% discount for every group of 10 seats purchased.

How much will the school pay for the new seats considering this tiered discount system with variable seat prices and discount rates?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$18,947.50}
Given the circle $O: x^2 + y^2 = 1$ and the functions $f(x) = x^3$, $f(x) = \tan(x)$, and $f(x) = x\sin(x)$, how many of these functions have graphs that can bisect the area of circle $O$ based on their symmetry properties? Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
Let \( ABC \) be a triangle and \( D, E \), and \( F \) be points located on segments \( AC, BA \), and \( CB \) respectively, such that the segments \( AF, BD \), and \( CE \) concur at a point \( P \) inside the triangle. It is given that \( BP=6, PD=6, PC=9, PE=3 \), and \( AF=20 \). Find the area of triangle \( ABC \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{108}
5. In an isosceles trapezoid $M N K L$ with bases $M L$, $N K$ the diagonals are perpendicular to the sides $M N, \quad K L$ and intersect at an angle of $22.5^{\circ}$. Find the height of the trapezoid if the length $N Q=3$, where $Q-$ is the midpoint of the larger base.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{3\sqrt{2-\sqrt{2}}}{2}}
There are 128 positive integers q with 3 digits that when divided by 7 leave a certain remainder. What is the remainder?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Let \( S = \{1, 2, 3, \ldots, 1990\} \), and let \( A \subset S \) with \( |A| = 26 \). If the sum of all elements in \( A \) is a multiple of 5, then \( A \) is called a "good subset" of 26 elements of \( S \). Find the number of "good subsets" of 26 elements of \( S \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{5} \binom{1990}{26}}
已知欧拉常数\gamma=\displaystyle\lim_{n\rightarrow+\infty}\left(1+\df{1}{2}+\df{1}{3}+\cdots+\df{1}{n}-\ln n\right)约等于 0.5772156649. 记 I=\df{100}{\displaystyle\int_0^1\left(\df{1}{x}-\left[\df{1}{x}\right]\right)\dd x}，则 [I]=__________.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{236}
Let the sequence $\{a_n\}$ have a sum of the first $n$ terms denoted by $S_n$. It is known that $4S_n = 2a_n - n^2 + 7n$ ($n \in \mathbb{N}^*$). Find $a_{11}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-2}
Sandra has 5 pairs of shoes in a drawer, each pair a different color. Every day for 5 days, Sandra takes two shoes out and throws them out the window. If they are the same color, she treats herself to a practice problem from a past HMMT. What is the expected value (average number) of practice problems she gets to do?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{5}{9}}
A 230 m long train running at a certain speed crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. The length of the other train is 270.04 m. What is the speed of the first train in km/hr?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{120.016}
Find the number of solutions to the equation \(x = \left\lfloor \frac{x}{2} \right\rfloor + \left\lfloor \frac{x}{3} \right\rfloor + \left\lfloor \frac{x}{5} \right\rfloor\), where \(\left\lfloor x \right\rfloor\) denotes the greatest integer less than or equal to \(x\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{30}
Jonathan eats 2500 calories every day except for Saturday, when he consumes an extra 1000 calories. He burns a certain amount of calories every day. His weekly caloric deficit is 2500 calories. How many calories does Jonathan burn daily?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3000}
The yearly changes in the population census of a city for five consecutive years are, respectively, 20% increase, 10% increase, 30% decrease, 20% decrease, and 10% increase. Calculate the net change over these five years, to the nearest percent.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-19\%}
Given a parabola $y = ax^2 + bx + c$ ($a \neq 0$) with its axis of symmetry on the left side of the y-axis, where $a, b, c \in \{-3, -2, -1, 0, 1, 2, 3\}$. Let the random variable $X$ represent the value of $|a-b|$. Calculate the expected value $E(X)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{8}{9}}
There are 10 individuals on a mysterious island, comprising both elves and wizards. Each person has a treasure chest containing a distinct number of gold coins ranging from 1 to 10. When asked about the number of gold coins in their chest, every wizard lies, while every elf tells the truth. If the reported numbers of gold coins are all within the range of 1 to 10 and the total sum of their reported gold coins is 36, then the island must have at least $\qquad$ wizards.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
In a circle with radius $6$, two chords $PQ$ and $RS$ intersect at a point $T$. Chord $RS$ bisects chord $PQ$ such that $PT = TQ = 8$ and $PQ$ is the only chord from $P$ that $RS$ bisects. It is known that the sine of the central angle subtended by minor arc $PR$ is a rational number. If expressed as a fraction $\frac{p}{q}$ in lowest terms, what is the product $pq$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{pq=20}
Given a triangle $\triangle ABC$ with side length $b = 2$ and angle $B = 60^\circ$, there are two possible solutions for the triangle. Determine the range of possible values for side length $a$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(2, \frac{4\sqrt{3}}{3})}
How many bitstrings of length 77 are there that start with 010 (i.e., have 010 at positions 1, 2, and 3) or have 101 at positions 2, 3, and 4, or have 010 at positions 3, 4, and 5?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2^75}
(5) The set of integer points on the plane $S=\{(a, b) \mid 1 \leqslant a, b \leqslant 5, a, b \in \mathbf{Z}\}$, $T$ is a set of integer points on the plane, such that for any point $P$ in $S$, there exists a point $Q$ in $T$ different from $P$, such that the line segment $P Q$ has no other integer points except $P$ and $Q$. How many elements does $T$ need to have at minimum? (Provided by Yonggao Chen)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
In an examination, 35% of the students passed, 25% of the students scored in the "B" grade range, and 481 students failed. How many students appeared for the examination?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{740}
一个六面体的各个面和一个正八面体的各个面都是边长为 $a$ 的正三角形, 这样两个多面体的内切球的半径之比是一个既约分数 $\frac{m}{n}$ .那么, 积 $m \cdot n$ 是  $\qquad$ .
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
In the bathhouse, a bathtub that can be filled with water up to 10 liters (L) is filled with water for the guests. 3 guests used 1 liter (L) and 500 milliliters (㎖) of water from this bathtub, and 1 guest used 1 liter (L) and 750 milliliters (㎖) of water. If the remaining guests each use 1 liter (L) and 250 milliliters (㎖) of water, how many people can take shower?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
某市发出车牌号码均由 6 个数字 (从 0 到 9 )组成, 但要求任意 2 个车牌至少有 2 位不同（如车牌 038471 和 030471 不能同时使用）。 求该市最多能发出多少个不同车牌？
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{100000}
Let \( P(x) \) be an \( n \)-degree polynomial such that
\[ P(x) = 2^{x}, \quad x = 1, 2, \cdots, n+1. \]

Find \( P(n+3) \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2 \left( 2^{n+2} - n - 3 \right)}
Find the number of ordered integer solutions (a, b, c) that satisfy the following system of equations:
|a+b| + c = 19 and ab + |c| = 97.
Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{12}
The sum of the digits of the result of the expression $\underbrace{99 \cdots 99}_{2021 \text{ digits}} \times \underbrace{99 \cdots 99}_{2020 \text{ digits}}$ is $\qquad$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{18189}
$n$ 个棋手参加象棋比赛，每两个棋手比赛一局. 规定：胜者得 1 分，负者得 0 分，平局各得 0.5 分。如果赛后发现任何 $m$ 个棋手中都有一个棋手胜了其余 $m-1$ 个棋手，也有一个棋手输给了其余 $m-1$ 个棋手，就称此赛况具有性质 $P(m)$ 。对给定的 $m(m \geqslant 4)$ ，求 $n$ 的最小值 $f(m)$ ，使得对具有性质 $P(m)$ 的任何赛况，都有所有 $n$ 名棋手的得分各不相同。请提供当m=10时，f(m)的值。
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{17}
A merchant placed on display some dresses, each with a marked price. He then posted a sign "$1/3$ off on these dresses." The cost of the dresses was $3/4$ of the price at which he actually sold them. Then the ratio of the cost to the marked price was:
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{2}}
Find the maximum value of the following expression:
$$
|\cdots||| x_{1}-x_{2}\left|-x_{3}\right|-x_{4}\left|-\cdots-x_{1990}\right|,
$$

where \( x_{1}, x_{2}, \cdots, x_{1990} \) are distinct natural numbers from 1 to 1990.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1989}
Represent the number 1000 as a sum of the maximum possible number of natural numbers, the sums of the digits of which are pairwise distinct.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{19}
设 $M=\{1,2, \cdots, 20\}, A_1, A_2, \cdots A_n$ 是 $M$ 的互不相同的非空子集, 当 $i \neq j$ 时, $A_i \cap A_j$ 至多有两个元, 求 $n$ 的最大值.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1350}
If the sum of the units digit, tens digit, and hundreds digit of a four-digit number $M$ is $12$, then this four-digit number $M$ is called an "eternal number." By swapping the thousands digit and hundreds digit of the "eternal number" $M$, and swapping the tens digit and units digit, we obtain a new four-digit number $N$. Let $F(M)=\frac{{M-N}}{9}$. If the difference between the hundreds digit and units digit of an "eternal number" $M$ is exactly the thousands digit, and $\frac{{F(M)}}{9}$ is an integer, then the maximum value of $F(M)$ is ____.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{9}
How many $5$-digit numbers $N$ (in base $10$) contain no digits greater than $3$ and satisfy the equality $\gcd(N,15)=\gcd(N,20)=1$? (The leading digit of $N$ cannot be zero.)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{256}
Triangle $ABC$ has $\angle A = 90^\circ$, $\angle C = 30^\circ$, and $AC = 12$. Let the circumcircle of this triangle be $W$. Define $D$ to be the point on arc $BC$ not containing $A$ so that $\angle CAD = 60^\circ$. Define points $E$ and $F$ to be the feet of the perpendiculars from $D$ to lines $AB$ and $AC$, respectively. Let $J$ be the intersection of line $EF$ with $W$, where $J$ is on the minor arc $AC$. The line $DF$ intersects $W$ at $H$ other than $D$. The area of the triangle $FHJ$ is in the form $\frac{a}{b}(\sqrt{c}-\sqrt{d})$ for positive integers $a,b,c,d$, where $a,b$ are relatively prime, and the sum of $a,b,c,d$ is minimal. Find $a+b+c+d$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{23}
On an island of Liars and Knights, a circular arrangement is called correct if each person in the circle can say that among their two neighbors, there is at least one member of their tribe. One day, 2019 natives formed a correct circle. A liar approached them and said, "Now we too can form a correct circle." How many knights could have been in the initial arrangement?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1346}
Given a right triangle $ABC$. On the extension of the hypotenuse $BC$, a point $D$ is chosen such that the line $AD$ is tangent to the circumcircle $\omega$ of triangle $ABC$. The line $AC$ intersects the circumcircle of triangle $ABD$ at point $E$. It turns out that the angle bisector of $\angle ADE$ is tangent to the circle $\omega$. In what ratio does point $C$ divide segment $AE$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1:2}
Kayla draws three triangles on a sheet of paper. What is the maximum possible number of regions, including the exterior region, that the paper can be divided into by the sides of the triangles?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{20}
Given that $F\_1$ and $F\_2$ are the left and right foci of the hyperbola $(x^{2}- \dfrac {y^{2}}{24}=1)$, and $P$ is a point on the hyperbola, find the area of $\triangle F\_1PF\_2$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{24}
12. B6 (FIN 3) Four distinct circles $C, C_{1}, C_{2}, C_{3}$ and a line $L$ are given in the plane such that $C$ and $L$ are disjoint and each of the circles $C_{1}, C_{2}, C_{3}$ touches the other two, as well as $C$ and $L$. Assuming the radius of $C$ to be 1 , determine the distance between its center and $L$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
A TV set worth Rs. 35,000 is to be paid in 36 installments of Rs. 2,300 each. If the rate of interest is 9% per annum compounded monthly, and the first installment is paid at the time of purchase, with an additional processing fee of Rs. 1,000 added to the last installment, what will be the value of the last installment covering the interest, principal, and processing fee?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3,300}
Given the circle O: $x^2+y^2=4$, and the equation of line $l$ is $x+y=m$. If there are exactly three points on circle O which are at a distance of 1 from line $l$, then the real number $m$ equals \_\_\_\_\_.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\pm\sqrt{2}}
A three-digit number has different digits in each position. By writing a 2 to the left of this three-digit number, we get a four-digit number; and by writing a 2 to the right of this three-digit number, we get another four-digit number. The difference between these two four-digit numbers is 945. What is this three-digit number?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{327}
Let $d_1 = a^2 + 2^a + a \cdot 2^{(a+1)/2} + a^3$ and $d_2 = a^2 + 2^a - a \cdot 2^{(a+1)/2} + a^3$. If $1 \le a \le 300$, how many integral values of $a$ are there such that $d_1 \cdot d_2$ is a multiple of $3$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{100}
How many pairs of positive integers $(a,b)$ are there such that the roots of the polynomial $x^2-ax-b$ are not greater than $5$? Provide the number of such pairs.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{50}
$39$ students participated in a math competition. The exam consisted of $6$ problems and each problem was worth $1$ point for a correct solution and $0$ points for an incorrect solution. For any $3$ students, there is at most $1$ problem that was not solved by any of the three. Let $B$ be the sum of all of the scores of the $39$ students. Find the smallest possible value of $B$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{165}
Let $\triangle ABC$ be a triangle with $AB=65$, $BC=70$, and $CA=75$. A semicircle $\Gamma$ with diameter $\overline{BC}$ is constructed outside the triangle. Suppose there exists a circle $\omega$ tangent to $AB$ and $AC$ and furthermore internally tangent to $\Gamma$ at a point $X$. The length $AX$ can be written in the form $m\sqrt{n}$ where $m$ and $n$ are positive integers with $n$ not divisible by the square of any prime. Find $m+n$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{76}
Find the minimum value of the expression \((\sqrt{2(1+\cos 2x)} - \sqrt{3-\sqrt{2}} \sin x + 1) \cdot (3 + 2\sqrt{7-\sqrt{2}} \cos y - \cos 2y)\). If the answer is not an integer, round it to the nearest whole number.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-9}
A metallic sheet with a thickness of 0.5 m is of rectangular shape with dimensions 48 m x 38 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, taking into account the material thickness, determine the volume of the open box (in m³).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5208}
An isosceles trapezoid has two rows of small identical isosceles triangles drawn along its top and bottom bases. Each small isosceles triangle has an area of 1. Find the area of the entire isosceles trapezoid.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}