Question

Mia found the area of a polygon The area is 32 square cm.

Which of these polygons has an area of 32 square cm?

Answer 1

Only the isosceles trapezoid has an area of 32 cm².

Explanation:

Let's calculate the area of each polygon.

For the two triangles we have:

`A_(t) = (bh)/(2) = (2 cm*4 cm)/(2) = 4 cm^(2)`

This polygon does not have an area of 32 cm².

For the rectangle we have:

`A_(r) = bh = 6 cm*4 cm = 24 cm^(2)`

This polygon does not have an area of 32 cm².

For the rectangle trapezoid we have:

`A_(rt) = A_(t) + A_(r) = (4 + 24) cm^(2) = 28 cm^(2)`

So, this polygon does not have an area of 32 cm².

Finally, for the isosceles trapezoid:

`A_(it) = A_(t)*2 + A_(r) = (4*2 + 24) cm^(2) = 32 cm^(2)`

This polygon does have an area of 32 cm².

Therefore, only the isosceles trapezoid has an area of 32 cm².

I hope it helps you!