Answer:
[tex]A=80\ ft^2[/tex]
Step-by-step explanation:
we know that
The area of the figure is equal to the area of an isosceles triangle (has two equal sides) plus the area of a rectangle
step 1
Find the area of the triangle
The area of the triangle is equal to
[tex]A=\frac{1}{2}bh[/tex]
we have
[tex]b=16\ ft[/tex]
To find out the height of the triangle Apply the Pythagorean Theorem
[tex]10^2=(16/2)^2+h^2[/tex]
solve for h
[tex]100=64+h^2[/tex]
[tex]h^2=100-64[/tex]
[tex]h^2=36[/tex]
[tex]h=6\ ft[/tex]
Find the area of triangle
[tex]A=\frac{1}{2}(16)(6)[/tex]
[tex]A=48\ ft^2[/tex]
step 2
Find the area of rectangle
The area of rectangle is equal to
[tex]A=LW[/tex]
we have
[tex]L=16\ ft\\W=2\ ft[/tex]
substitute
[tex]A=(16)(2)=32\ ft^2[/tex]
step 3
Find the area of the figure
Adds the areas
[tex]A=48+32=80\ ft^2[/tex]
