Question

A bookmark is shaped like a rectangle with a semicircle attached at both ends. The rectangle is 14 cm long and 4 cm wide. The diameter of each circle is the width of the rectangle. What is the area of the bookmark? Use 3.14 for π.

Answer 1

The area of the bookmark is 68.56 cm².

Explanation:

Separate the bookmark into simpler shapes as described in the problem: a rectangle and a circle (two semicircles of the same size).

Find the area of the simpler figures.

Rectangle

A = LW

A = 14 · 4

A = 56

The area of the rectangle is 56 cm2.

Circle

A = πr2

A = 3.14(2)2

A = 3.14(4)

A = 12.56

The area of the circle is 12.56 cm2.

Find the area of the bookmark.

A = 56 + 12.56

A = 68.56

The area of the bookmark is 68.56 cm².

Answer 2

First you must find the area of the rectangle:

14 x 4 = 56cm^2

Then you must find the area of the semicircles:

Because there are two semicircles you need to find the area of one full circle.

n = pi
A =nr^2
A=n x 2^2
A=4n
A= 4 x 3.14
A= 12.56

Add the area together:

12.56 + 56
=68.56cm^2