   Chapter 8.CR, Problem 8CR Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Find the area and the perimeter of a rhombus whose diagonals have lengths 18 in. and 24 in.

To determine

To find:

The area and perimeter of the rhombus.

Explanation

The area A of a rhombus whose diagonals have lengths d1 and d2 is given by

A=12d1d2

In the case of a rhombus, all four sides are the same length by definition, so the perimeter is four times the length of a side. Or as a formula:

Perimeter = 4S, where S is the length of any one side.

Calculation:

Given: A rhombus whose diagonals have lengths 18 in. and 24 in.

Let ABCD be a rhombus whose diagonals AC = 18 in and BD = 24 in.

To find the length of side of the rhombus:

In the above picture, you can see a rhombus with its diagonals bisecting themselves. ADE has a right angle.

Using Pythagorean Theorem, you calculate the side of rhombus AD like this:

Where AC and BD are length of the diagonals.

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