Question

A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 29ft long and 18ft wide. If the gardener wants to build a fence around the garden, how many feet of fence are required? Use the value 3.14 for, and do not round your answer. Be sure to include the correct unit in your answer

Answer 1

The area of the garden is

797

f

t

2

.

Step-by-step explanation:

First, let's find the area of the rectangle.

We know that the area of a rectangle is the length times width, or

20

⋅

32

in this example:

20

⋅

32

=

640

So the area of the rectangle is

640

f

t

2

.

You may not know the area of a semicircle, but that's fine

−

we know the area of a circle, or

π

r

2

.

Since the area of a semicircle is half the area of a circle, we just do the area of the circle divided by

2

:

So the area of a semicircle is

π

r

2

2

.

The question asks for

π

to just be

3.14

, so instead the equation is

A

=

3.14

r

2

2

The picture gives the diameter of the circle.

To find the radius, or

r

, we divide the diameter by

2

:

20

2

=

10

Now we can solve for the area of the semicircle:

3.14

(

10

)

2

2

3.14

(

100

)

2

314

2

157

f

t

2

Now that we now the areas of the rectangle and semicircle, we can add them up to find the area of the rose garden:

640

+

157

=

797

f

t

2