Answer:
A = 44 cm²
Step-by-step explanation:
The area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height and b₁, b₂ the parallel bases
We require to find the missing segment of b₁
Using the tangent ratio in the right triangle
tan45° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{4}{adjacent}[/tex] = 1 , so
adjacent = 4
Then
b₁ = 4 + 8 + 2 = 14 , b₂ = 8 and h = 4 , then
A = [tex]\frac{1}{2}[/tex] × 4 × (14 + 8) = 2 × 22 = 44 cm²
