How would you find the area without the height of the triangle?

Accepted Solution

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 - baseh - heightWe 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 - lengthw - widthWe 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]