Atividades de PERÍMETRO e ÁREA
Autor: Denise MCO | Publicado: 2012-11-05T18:20:00-02:00




&nbsp; &nbsp; &nbsp; &nbsp;1.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
A malha quadriculada é formada por quadradinhos
de lados que medem uma unidade de comprimento. Adotando a medida do lado de um quadradinho como
unidade, determine o perímetro de cada figura da malha.

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&nbsp;2.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Quanto mede o perímetro do pentágono equilátero
com medida de lado = 12 cm?





3.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Determine a área das figuras a seguir,
considerando 1 quadradinho como unidade de medida de área.

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<!--[if !supportLists]-->&nbsp; &nbsp; &nbsp; &nbsp;4.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <!--[endif]-->Quanto
mede o lado de um octógono equilátero cujo perímetro é igual a 120 cm?



<!--[if !supportLists]-->&nbsp; &nbsp; &nbsp; &nbsp;5.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <!--[endif]-->Maurício
tem um terreno e pretende cercá-lo com arame farpado. O terreno tem forma
retangular com medidas de 60 m por 30 m. Considerando que Maurício quer que a
cerca tenha 5 voltas, quantos metros de arame farpado serão necessários?



<!--[if !supportLists]-->&nbsp; &nbsp; &nbsp; &nbsp;6.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <!--[endif]-->Um
triângulo equilátero e um pentágono equilátero têm perímetros iguais. Se o lado
do triângulo é igual a 10 dm, quanto mede o lado do pentágono?



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 10
dm &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;?



<!--[if !supportLists]-->&nbsp; &nbsp; &nbsp; &nbsp;7.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->Na malha quadriculada abaixo, desenhe o que é
pedido em cada item, considerando o lado e a unidade de um quadradinho como
unidades de medida de comprimento e área, respectivamente.





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<!--[if !supportLists]-->&nbsp; &nbsp; &nbsp;a)&nbsp;&nbsp;&nbsp; <!--[endif]-->Um
quadrilátero com 2 unidades de área.

<!--[if !supportLists]-->&nbsp; &nbsp; &nbsp;b)&nbsp;&nbsp; <!--[endif]-->Um
polígono com 12 unidades de perímetro.



<!--[if !supportLists]-->&nbsp; &nbsp; &nbsp; &nbsp;8.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <!--[endif]-->Na
aula de Educação Física o professor Guilherme pediu que os alunos se aquecessem
correndo quatro voltas em torno da quadra de futebol de salão. Sabendo que a
quadra tem 40 metros de comprimento e 20 metros de largura, quantos metros
correram os alunos que fizeram o aquecimento até o final?



&nbsp; &nbsp; &nbsp; &nbsp;9.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <!--[endif]-->Um
salão quadrangular tem 48 m de perímetro. Um quintal retangular, cujo
comprimento mede 16 m, tem o mesmo perímetro que o salão. Qual é a largura
desse quintal?



&nbsp; &nbsp; &nbsp; 10.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Determine
a área das figuras na malha quadriculada abaixo e complete a tabela..

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<!--[if !supportLists]-->&nbsp; &nbsp; &nbsp; 11.&nbsp;&nbsp; <!--[endif]-->Todas
a figuras abaixo foram construídas com 6 quadrados de área de 1 cm2.





&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
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<!--[if !supportLists]-->&nbsp; &nbsp; &nbsp; 12.&nbsp;&nbsp;
<!--[endif]-->Observe as figuras na malha quadriculada.



Considere cada quadradinho como
unidade de medida para determinar qual das figuras tem a maior área.



<!--[if !supportLists]-->&nbsp; &nbsp; &nbsp; 13.&nbsp;&nbsp; <!--[endif]-->Calcule
a área da região mostrada na figura, sabendo que a malha quadriculada é formada
por quadradinhos que representam uma área de 1m2.





Confira suas respostas:



GABARITO



<!--[if !supportLists]-->1.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->Lembre-se de que o perímetro de uma figura é
igual a soma de seus lados.

<!--[if !supportLists]-->a)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->2 + 2 + 2 + 1 + 4 + 3 = 14 unidades

<!--[if !supportLists]-->b)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 +
= 12
unidades

<!--[if !supportLists]-->c)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->1 + 1 + 2 + 1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 + 1 + 2
+ 1 + 2 = 22 unidades

<!--[if !supportLists]-->d)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->2 + 4 + 2 + 4 = 12 unidades

<!--[if !supportLists]-->e)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->1 + 2 + 2 + 2 + 1 + 1 + 1 + 2 + 2 + 2 +1 + 1 + 2
+ 4 = 24 unidades

<!--[if !supportLists]-->f)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->1 + 2 + 1 + 1 + 2 + 1 + 1 + 1+ 1 + 1 = 12
unidades



<!--[if !supportLists]-->2.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->12 cm + 12 cm + 12 cm + 12 cm + 12 cm = 12 cm x
5 = 60 cm

&nbsp; &nbsp; &nbsp; &nbsp;O perímetro do pentágono é 60 cm.

<!--[if !supportLists]-->3.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->&nbsp;

<!--[if !supportLists]-->&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
I.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->0,5 + 2 + 0,5 + 0,5 + 4 + 0,5 + 4 + 4 = 16
quadradinhos

<!--[if !supportLists]-->&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
II.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->0,5 + 3 + 0,5 + 0,5 + 5 + 0,5 + 0,5 + 7 + 0,5 +
6 + 6 + 6 = 36 quadradinhos



<!--[if !supportLists]-->4.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->Sabemos que o perímetro é a soma dos lados da
figura e que um octógono equilátero possui 8 lados iguais, portanto a medida de
um dos lados da figura = 120 : 8&nbsp; a
15

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; O lado do octógono mede 15 cm.



<!--[if !supportLists]-->5.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->O perímetro do terreno é igual a 60 + 30 + 60 +
30 = 180 m

Para que a cerca dê 5 voltas no
terreno são necessários 5 . 180 = 900 m de arame farpado.



<!--[if !supportLists]-->6.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->O perímetro do triângulo é 10 dm + 10 dm + 10 dm
= 30 dm

Se o perímetro das 2 figuras é
igual e o pentágono equilátero tem 5 lados iguais; então o lado do pentágono =
30 : 5 a
6

O lado do pentágono mede 6 dm.



<!--[if !supportLists]-->7.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->Respostas possíveis

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<![endif]--><!--[if !vml]--><!--[endif]-->a)&nbsp;





b)

&nbsp;





















<!--[if !supportLists]-->8.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->O perímetro da quadra é igual a 40 + 20 + 40 +
20 = 120 m

Para completar o aquecimento os
alunos devem dar 4 voltas na quadra, portanto 4 . 120 = 480 m

Os alunos que fizeram o aquecimento
até o final correram 480 m.



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<!--[if !supportLists]-->9.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->Sabemos que o quintal é retangular, portanto os
lados a = a&nbsp; e b = b

Já que conhecemos o comprimento
do quintal, 16 m &nbsp;já possuímos as medidas
de dois dos lados, e sua&nbsp;soma é 16 + 16 = 32 m. Se o
perímetro do quintal é 48m, a soma dos lados restantes é 48 - 32 = 16 m.&nbsp;Como o quintal é retangular,
esses dois lados têm a mesma medida, portanto 16 : 2 = 8 m

Então: A largura desse quintal mede 8m.



<!--[if !supportLists]-->10.&nbsp;&nbsp;
<!--[endif]-->&nbsp;

 

  
Figura

  
1

  
2

  
3

  
4

  
5

  
6

  
7

 

  
área (cm2)

  
15

  
8

  
27

  
8

  
19

  
9

  
12

 








<!--[if !supportLists]-->11.&nbsp;&nbsp;
<!--[endif]-->&nbsp;

 

  
Figura

  
1

  
2

  
3

  
4

  
5

  
6

  
7

 

  
perímetro(cm2)

  
10

  
12

  
14

  
12

  
14

  
14

  
14

 








<!--[if !supportLists]-->12.&nbsp;&nbsp;
<!--[endif]-->&nbsp;

<!--[if !supportLists]-->&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
I.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->área =8 unidades

<!--[if !supportLists]-->&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
II.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->área = 9 unidades

<!--[if !supportLists]-->&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
III.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->área = 14 unidades

<!--[if !supportLists]-->&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
IV.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->área = 14 unidades

Portanto: As alternativas III e IV são as figuras com
maior área.



<!--[if !supportLists]-->13.&nbsp;&nbsp;
<!--[endif]-->0,5 + 1 + 2 + 0,5 + 1 + 0,5 = 5,5

A área da região da figura é de 5,5 m2






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