Question

Find the area and perimeter of the shape below. Each semicircle has a radius of 3 units. Problem 2 For each problem, decide whether the circumference of the circle or the area of the circle

Answer 1

The area of the shape is
`\(18\pi + (9)/(2)\)` square units, and the perimeter is
`\(18 + 9\pi\)` units.

Step-by-step explanation:

To find the area, we need to calculate the sum of the areas of the rectangle and the two semicircles. The rectangle has dimensions 6 units by 3 units, so its area is
`\(6 * 3 = 18\)` square units. Each semicircle has a radius of 3 units, so their combined area is
`\(2 * (1)/(2) \pi r^2 = 2 * (1)/(2) \pi * 3^2 = 18\pi\)` square units. Therefore, the total area is
`\(18 + 18\pi\)` square units.

For the perimeter, we need to find the sum of the lengths of all the sides. The rectangle has a perimeter of
`\(2 * (6 + 3) = 18\)` units. The semicircles contribute to the perimeter as well. Since each semicircle is along the length of the rectangle, their combined arc length is equal to the length of the rectangle. Thus, the total perimeter is
`\(18 + 9\pi\)` units.

In summary, the area is
`\(18 + 18\pi\) square units, and the perimeter is \(18 + 9\pi\)` units for the given shape with semicircles of radius 3 units.