Question

A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 29 ft long and 20 ft wide.

Find the area of the garden. Use the value 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer.

Answer 1

15.7 square feet

Explanation:

To find the area of the garden we find the area of the rectangle and the area of the semicircle.

The area of the rectangle:

A=bh

A=(29)(20)

A=580ft^2

As shown in the picture, the width of the rectangle is 20 ft wide, which means that the diameter of the semicircle is also 20ft wide. The diameter is two times the radius, which means the radius of the semicircle is 10ft.

The area of a circle is represented by the equation:
`A=\pi r^(2)`

A semicircle is half of a circle, therefore the equation to find the area of a semicircle is:
`A=(1)/(2)\pi r^(2)`

Plugging our radius of 10ft in we get:

`A=(1)/(2)\pi (10)\\ A=5\pi`

We use 3.14 for our value of
`\pi` to get:

`A=5(3.14)\\A=15.7ft^(2)`

Therefore, the area of the rose garden is 15.7 square feet.