Answer:
Only the isosceles trapezoid has an area of 32 cm².
Step-by-step explanation:
Let's calculate the area of each polygon.
For the two triangles we have:
![A_{t} = \frac{bh}{2} = \frac{2 cm*4 cm}{2} = 4 cm^{2}](https://tex.z-dn.net/?f=%20A_%7Bt%7D%20%3D%20%5Cfrac%7Bbh%7D%7B2%7D%20%3D%20%5Cfrac%7B2%20cm%2A4%20cm%7D%7B2%7D%20%3D%204%20cm%5E%7B2%7D%20)
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}](https://tex.z-dn.net/?f=%20A_%7Br%7D%20%3D%20bh%20%3D%206%20cm%2A4%20cm%20%3D%2024%20cm%5E%7B2%7D%20)
This polygon does not have an area of 32 cm².
For the rectangle trapezoid we have:
So, this polygon does not have an area of 32 cm².
Finally, for the isosceles trapezoid:
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!