First, you have to calculate the height of the trapezoid, using:
h = c * sin(α) = 4 * sin(30°) = 2.
Now using the Pythagorean theorem we can find the values of the projections of the sides on the base a:
sqrt(c² - h²) = sqrt(16 - 4) = 3.46 and sqrt(d² - h²) = 2.24.
Subtract these values from the base a to find b:
b = a - sqrt(c² - h²) - sqrt(d² - h²) = 10 - 3.46 - 2.24 = 4.3
and then the perimeter:
P = 10 + 4 + 3 + 4.3 = 21.3
Read more