Question

A rectangular piece of paper with length 24 cm and width 12 cm has two semicircles cut out of it, as shown below. Find the area of the paper that remains. Use the value 3.14 for n, and do not round your answer. Be sure to include the correct unit in your answer.

Answer 1

To determine the area of the remaining paper, you have to subtract the area of the semicircle ( i.e. the area of a full circle) from the area of the rectangle.

Recall that the area of a circle is given by the following formula:

`A_c=\pi r^2,`

where r is the radius. Now, the semicircles have a radius of 12cm/2=6cm, therefore, the area of the circle formed by the semicircles is:

`Ac=\pi(6cm)^2=3.14(36cm^2)=113.04cm^2.`

The area of a rectangle is given by the following formula:

`A_r=wl,`

where w=width, and l=lenght. Therefore, the area of the rectangle is:

`A_r=(24cm)(12cm)=288cm^2.`

Finally, the area of the remaining paper is:

`288cm^2-113.04cm^2=174.96cm^2.`

Answer:

`174.96cm^2.`