Question

Find the area of the figure. Round to the nearest tenth.

A 23.4 ft^2
B 28.3 ft^2
C 29.7 ft^2
D 36.0 ft^2

Answer 1

C

Explanation:

What is the area?

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

What is diameter?

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

To solve for the area of a rectangle we use the expression:

• A = length × width

Inserting the dimensions of the rectangle:

• 4 × 4 = 36

So, the area of the rectangle is 36 square feet.

Because the rectangle has a gap on the left side in the shape of a semicircle, we can first solve for the area of that semicircle.

How do we solve for the area of a semicircle?

if you know the radius of a semicircle, you can use the formula:

`A = (\pi r^(2) )/(2)`

But first, we need to solve for the radius.

Because the diameter is twice the size of the radius, we can use this expression:

• 4 ÷ 2 = 2

So, the radius of the semicircle is 2ft.

Inserting 2 into the formula for r:

• 
  `A = (\pi 2^(2) )/(2)`

First, we need to evaluate the exponent:

• 
  `A = (\pi 2^(2) )/(2) = (\pi4)/(2)`

Dividing 4 by 2 gives:

• 
  `\pi2`

This simplifies to:

• 6.28319

Subtracting that from the area of the rectangle:

36 - 6.28319 = 29.71681 =
`29.7ft^(2)` (Rounded to the nearest tenth)

Therefore, the answer is C.