Question

Find the area of a rhombus having perimeter 80 cm and one diagonal 24 cm.
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Answer 1

A=384cm²

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Answer 2

$\huge \fbox \red{Answer}$

Perimeter of a rhombus = 80 m (given)

We know, Perimeter of a rhombus = 4 x side

Let a be the side of a rhombus.

4 x a = 80

a = 20

One of the diagonal,

AC = 24 m (given)

Therefore OA = 1/2 x AC

OA = 12

In △AOB,

Using Pythagoras theorem:

OB² = AB² − OA²

= 20² −12²

= 400 – 144

= 256

OB = 16

Since diagonal of rhombus bisect each other at 90 degrees.

And OB = OD

Therefore, BD = 2 OB

= 2 x 16 = 32 m

Area of rhombus = 1/2 x BD x AC

= 1/2 x 32 x 24

= 384

Hence, Area of rhombus = 384 m²