Question

Find the area and perimeter

Answer 1

Answer: area = 379.7 mm²

Perimeter = 95.84 mm

Step-by-step explanation:

The composite shape contains a semi circle and a trapezoid.

The area of a semi circle is

1/2 × πr²

Radius = diameter/2

Radius = 20/2 = 10 mm

Area = 1/2 × 3.14 × 10 = 15.7 mm²

Area of trapezoid is expressed as

1/2(a + b)h

Area = 1/2 × (20 + 32)14

Area = 1/2 × 52 × 14) = 364mm²

Area of the composite shape is

15.7 + 364 = 379.7 mm²

Formula for determining the perimeter of the semicircle is

1/2 × πd

Perimeter = 1/2 × 3.14 × 20 = 31.4mm

Looking at the attached photo, we would determine the slant height,h, by applying Pythagorean theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

h² = 12² + 14² = 340

h = √340/= 18.44

Perimeter of the composite shape is

31.4 + 14 + 32 + 18.44 =95.84 mm