For this case we must find the area of the figure composed of a triangle and a rectangle.
Triangle area:
[tex]A_ {t} = \frac {b * h} {2}[/tex]
Where b is the base and h is the height.
Area of the rectangle:
[tex]A_ {r} = a * b[/tex]
Where a and b are the sides.
The base of the triangle measures:
[tex]13-5 = 8[/tex]
We find the height by trigonometry:
[tex]tg (45) = \frac {h} {b}\\1 = \frac {h} {b}\\b = h[/tex]
So:
[tex]A_ {t} = \frac {8 * 8} {2}\\A_ {t} = 32 \ ft ^ 2[/tex]
On the other hand:
[tex]A_ {r} = 5 * 8\\A_ {r} = 40 \ ft ^ 2[/tex]
Thus, the total are the sum:
[tex](32 + 40) ft ^ 2 = 72 \ ft ^ 2[/tex]
Answer:
Option A
