Question

Type the correct answer in the box. Assume that pi=3.14 and round to the nearest hundredth.

The figure shown is formed by the arcs joining the midpoints of the four sides of a square with a side length of 15 centimeters.

The area of the shape is (blank) square centimeters.

Answer 1

White area = \[\frac{15^2\pi}{4}\] Shaded area = \[15^2-\frac{15^2\pi}{4}\]

Answer 2

The area of shape is: 48.38 square centimeters

Explanation:

The area of the shape is the area of the square minus the sum of the area of four half semicircles.

We know that four half semicircles will be equal to one circle.

Hence, the area of shape is:

Area of square-Area of circle.

We know that the area of a square with side length s is calculated by:

`\text{Area\ of\ square}=s^2`

Also, the area of a circle with radius r is calculated by using the formula:

`\text{Area\ of\ circle}\pi r^2`

Here the side length of the square i.e. s=15 cm.

and the radius of the circle i.e. r=15/2 cm

Hence,

`\text{Area\ of\ square}=(15)^2`

i.e.

`\text{Area\ of\ square}=225\ cm^2`

and

`\text{Area\ of\ circle}=3.14* ((15)/(2))^2`

i.e.

`\text{Area\ of\ circle}=176.625\ cm^2`

Hence, The area of shape is:

`\text{Area\ of\ shape}=225-176.625`

i.e.

`\text{Area\ of\ shape}=48.375\ cm^2`