Answer:
[tex]\large\boxed{B.\ 1,024\ ft^2}[/tex]
Step-by-step explanation:
It's an equaliteral triangle. Therefore, the height divides the base in half.
Use the Pyhagorean theorem:
[tex]h^2+\left(\dfrac{32}{2}\right)^2=20^2[/tex]
[tex]h^2+16^2=20^2[/tex]
[tex]h^2+256=400[/tex] subtract 256 from both sides
[tex]h^2=144\to h=\sqrt{144}\\\\h=12\ ft[/tex]
The formula of an area of a triangle:
[tex]A_\triangle=\dfrac{bh}{2}[/tex]
b - base
h - height
We have b = 32 ft and h = 12 ft. Substitute:
[tex]A_\triangle=\dfrac{(32)(12)}{2}=(16)(12)=192\ ft^2[/tex]
The formula of an area of a rectangle:
[tex]A_{\boxed{\ }}=lw[/tex]
l - length
w - width
We have l = 32 ft and w = 26 ft. Substitute:
[tex]A_{\boxed{\ }}=(32)(26)=832\ ft^2[/tex]
The area of the figure:
[tex]A=A_\triangle+A_{\boxed{\ }}\\\\A=192+832=1,024\ ft^2[/tex]
