Question

A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 32 ft long and 20 ft wide. Find the area of the garden? Use the value 3.14 for pie and do not round your answer.

Answer 1

The area of the garden is `797 ft^2`.

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 ft^2`.

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You may not know the area of a semicircle, but that's fine `-` we know the area of a circle, or `pir^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 `(pir^2)/2`.

The question asks for `pi` to just be `3.14`, so instead the equation is `A = (3.14r^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 ft^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 ft^2`