Answer:
- perimeter: 40.48 mm
- area: 110.55 mm²
Explanation:
You want the perimeter and area of a composite figure that has an isosceles triangle atop a semicircle of diameter 12 mm. The triangle's height is 9 mm.
Perimeter
The length of the semicircle is half the circumference of the circle with the same diameter:
C = 1/2πd . . . . circumference of semicircle
C = 1/2π(12 mm) = 6π mm ≈ 18.85 mm
When the two straight sides are added, the perimeter is found to be ...
P = (2×10.82 +18.85) mm ≈ 40.48 mm
The perimeter of the figure is about 40.48 mm.
Area
The area is the sum of the areas of the triangle and the semicircle:
A = 1/2bh +1/2πr²
A = 1/2(12 mm)(9 mm) +1/2π(6 mm)² = 1/2(108 mm² +36π mm²)
A = (54 +18π) mm² ≈ 110.55 mm²
The area of the figure is about 110.55 mm².