Question

A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 23 ft long and 14 ft wide.
Find the area of the garden. Use the value 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.

Answer 1

Answer:

629.72 square feet

Step-by-step explanation:

The area of the garden is the sum of the area of the rectangle and the area of the semicircle.

The area of the rectangle is length times width, so:

Area_rectangle = 23 ft * 14 ft = 322 ft²

The area of a circle is πr², but since we have a semicircle (half of a circle), we divide this by 2. The radius of the semicircle is the same as the width of the rectangle, which is 14 ft. So:

Area_semicircle = 1/2 * π * (14 ft)² = 1/2 * 3.14 * 196 ft² = 307.72 ft²

Adding these together gives the total area of the garden:

Area_garden = Area_rectangle + Area_semicircle = 322 ft² + 307.72 ft² = 629.72 ft²

So, the area of the garden is 629.72 square feet.