A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 28ft long and 18ft wide.Find the area of the garden. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.18ft28ft
Question
A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 28ft long and 18ft wide.Find the area of the garden. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.18ft28ft
Solution
To find the total area of the garden, we need to find the area of the rectangle and the area of the semicircle separately, then add them together.
Step 1: Find the area of the rectangle. The formula for the area of a rectangle is length x width. So, the area of the rectangle is 28ft x 18ft = 504 square feet.
Step 2: Find the area of the semicircle. The formula for the area of a circle is πr². However, since we only have a semicircle (half of a circle), we will need to divide this by 2. The radius of the semicircle is half the width of the rectangle, which is 18ft / 2 = 9ft. So, the area of the semicircle is (3.14 x (9ft)²) / 2 = 127.26 square feet.
Step 3: Add the areas together. The total area of the garden is the area of the rectangle + the area of the semicircle = 504 square feet + 127.26 square feet = 631.26 square feet.
So, the area of the garden is 631.26 square feet.
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