Question

A rectangular piece of paper with length 34 cm and width 16 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

First, we find the total area of the rectangle and then subtract the area of the two semicircles.

Area of rectangle:

$A=width\times length$

Where:

width = 16 cm

length = 34 cm

Substitute the values:

$A=16\times34=544$

We have that 2 semi-circles make a whole circle, and the area for the circle follows the formula:

$A=\frac{\pi d^2}{4}$

Where:

d = diameter = 16 cm

pi = 3.14

Substitute the values:

$A=\frac{(3.14)(16)^2}{4}=\frac{(3.14)(256)}{4}=(3.14)(64)=200.96$

Therefore, the area of the paper that remains is given by:

$A=544-200.96=343.04$

Answer: 343.04 cm^2