Question

Warm-Up

What is the approximate area of the shaded region?
Select the correct answer.
O 15.45 cm²
O69.53 cm²
128.54 cm²
18 cm
182.47 cm²
4

Answer 1

The answer is 69.63cm²

Explanation:

d=18

r=d/2=18/2=9cm

Area of shaded portion =Area of square -Area of circle

A=18²-pi×9²

A=69.53cm²

Answer 2

69.53 centimeters squared.

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.

To solve for the area of the shaded region, we must figure out what the length and width is. Assuming this is a square, the length and width of the shape are 18cm. To solve for the area of a square, we can use the formula:

• Area =
  `side^(2)`

Inserting 18 as our side length:

• Area =
  `18^(2)` = 324

Therefore, the area of the square without the circular gap is 324
`cm^(2)`.

To solve for the area of a circle, we can use the formula:

• Area = π
  `r^(2)`

But wait, we are given the diameter, not the radius!

No worries, the radius is simply half the size of the diameter, so we can just divide 18 by 2.

• 18 ÷ 2 = 9

Inserting 9 into the formula for the radius:

• Area = π ×
  `9^(2)` = 81π = 254.47 (Rounded to 2 decimal points)

Now we can subtract this from the squares area.

• 324 - 254.47 = 69.53

The closest to match this approximation is
`69.53cm^(2)`.