Answer:
B. 114 cm²
Explanation:
You want to know the area of a complex shape consisting of a triangle and a semicircle.
Areas of Parts
The shape can be divided at the dotted line into two shapes whose areas you have formulas for:
- semicircle of radius 5 cm
- triangle with base 15 cm and height 10 cm
Using the formulas for their areas, we find the area of each shape to be ...
A = (1/2)πr² . . . . . . area of semicircle with radius r
A = (1/2)π(5 cm)² = 25/2π cm² ≈ 39 cm²
A = (1/2)bh . . . . . . area of triangle with base b and height h
A = (1/2)(15 cm)(10 cm) = 75 cm²
Total area
The sum of the areas of the parts is ...
total area = semicircle area + triangle area
total area = 39 cm² +75 cm²
total area = 114 cm²
The area of the complex shape is about 114 cm².