5.
A rectangle, a triangle, and two congruent semicircles were used to form the figure shown.
8 centimeters, 6 centimeters, 4 centimeters, 3 centimeters
Which measurement is closest to the area of the figure in square centimeters?
67 cm²
74 cm²
79 cm²
88 cm²
The area of the figure can be calculated by finding the sum of the areas of the rectangle, triangle, and two congruent semicircles.
The area of the rectangle = 8 cm * 6 cm = 48 cm²
The area of the triangle = 1/2 * base * height = 1/2 * 4 cm * 3 cm = 6 cm²
The area of a semicircle = 1/2 * π * (radius)²
For each semicircle:
Radius = 4 cm / 2 = 2 cm
Area = 1/2 * π * (2 cm)² = 2π cm²
Total area = 48 cm² + 6 cm² + 2(2π cm²) = 48 cm² + 6 cm² + 4π cm²
≈ 74.13 cm²
Therefore, the measurement closest to the area of the figure in square centimeters is 74 cm².