Let's break apart the arrow shape into one triangle and another square.
We will find the area of the triangle and the square separately, then add them to find the area of the composite figure (arrow).
Let's break apart the arrow and see the image shown below:
Area of Triangle
The area of a triangle is given by the formula:
[tex]A=\frac{1}{2}bh[/tex]
Where
b is the base length
h is the height
Given,
base = 2 + 6 + 2 = 10 ft
height = 12 ft
We find the area of the triangle to be:
[tex]\begin{gathered} A=\frac{1}{2}bh \\ A=\frac{1}{2}(10)(12) \\ A=\frac{1}{2}(120) \\ A=60 \end{gathered}[/tex]
Now, Area of Square:
The area of a square is given by the formula:
[tex]A=s^2[/tex]
Where
s is the side length of the square
Given,
s = 6 ft, so the area of the square is:
[tex]\begin{gathered} A=s^2 \\ A=6^2 \\ A=36 \end{gathered}[/tex]
Total Area of the Composite Figure is:
60 + 36 = 96 sq. ft.
The 2nd option is correct, 96 sq. ft.
