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:
[tex] A_{t} = \frac{bh}{2} = \frac{2 cm*4 cm}{2} = 4 cm^{2} [/tex]
This polygon does not have an area of 32 cm².
For the rectangle we have:
[tex] A_{r} = bh = 6 cm*4 cm = 24 cm^{2} [/tex]
This polygon does not have an area of 32 cm².
For the rectangle trapezoid we have:
[tex] A_{rt} = A_{t} + A_{r} = (4 + 24) cm^{2} = 28 cm^{2} [/tex]
So, this polygon does not have an area of 32 cm².
Finally, for the isosceles trapezoid:
[tex] A_{it} = A_{t}*2 + A_{r} = (4*2 + 24) cm^{2} = 32 cm^{2} [/tex]
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!
