Answer:
81.75 ft²
Step-by-step explanation:
The area (A) of a trapezoid is calculated using the formula
A = [tex]\frac{1}{2}[/tex] h (a + b)
where a, b are the parallel bases and h is the perpendicular height
Calculate h using the right triangle and the sine ratio
sin30° = [tex]\frac{opposite }{hypotenuse}[/tex] = [tex]\frac{h}{10}[/tex]
Multiply both sides by 10
10 × sin30° = h, thus
h = 5
a = 12 and b = 8.7 + 12 = 20.7, hence
A = [tex]\frac{1}{2}[/tex] × 5 × (12 + 20.7)
= 0.5 × 5 ×32.7
= 81.75 ft²
