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!!!

Guest Apr 10, 2021

#1**0 **

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. :))

=^._.^=

catmg Apr 10, 2021