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Chapter 11: Q17. (page 431)

Find the area of each figure:

A rhombus with perimeter and one diagonal 30 .

Short Answer

Expert verified

The area of given figure is 240 square units.

Step by step solution

01

Step 1. Given information.

Perimeterp=68 and one diagonal d1=30.

02

Step 2. Analyze the given information.

As the all four sides are equal in length in rhombus.

Let common side be a and Perimeter is 68 ,

Then, we can saya+a+a+a=68

4a=68

a=17

03

Step 3. Find the other diagonal of rhombus.

We can use Pythagoras theorem.

Pythagorean Theorem define that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of other sides.

172=152+x2

x2=289鈭�225

x2=64

x=8

So the other diagonal will be 8+8=16

04

Step 4. Find the area of given figure.

Area of rhombus can be found using the formula

A=12d1d2

Where,

d1andd2are the diagonals of arhombus

A=12d1d2

=12脳30脳16

=30脳8

= 240 Square units.

Therefore, the area of given figure is240 square units.

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