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The trapezoid shown has a height of length $12\text{ cm},$ a base of length $16\text{ cm},$ and an area of $162\text{ cm}^2.$ What is the perimeter of the trapezoid?

 

Tysm in advance!!! I really need help... I don't think my teacher said enough, and it's not office hours. Thanks so so much!!!

 Apr 10, 2021
 #1
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I'd love to help. 

b_1 = 16

b_2 = x

h = 12

a = 162. 

The area of a trapazoid is the average of the bases * height. 

(b_1+b_2)/2*h = a

(16+x)/2*12 = 162

16+x = 27

x = 11

 

So now we know the 2 bases. 

For sake of simplicity, we'll just make the trapazoid look like a rectnagle with a triangle at the end. 

___

|      \

|        \

----------

 

Should look smth like that. 

We know 3 of the sides alr, the height and the 2 bases, and we can use the pythagreon theorum. 5^2+12^2 = 13^2. 

So our sides are 13 + 11 + 16 + 12 = 52

 

I hope this helped. :))

 

=^._.^=

 Apr 10, 2021
 #2
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Oh my- thank you so so much! I understand it now :D

 Apr 11, 2021

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