Question

16.
Find the area of a rhombus having perimeter 80 cm and one diagonal 24 cm.
(2) 364 sq. cm
(1)
(4)
354 sq. cm
384 sq. cm
480 sq. cm write
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Answer 1

Given:

Perimeter of rhombus = 80 cm

Length of one diagonal = p = 24 cm

To find:

Area of the rhombus = ?

Solution:

Area of rhombus = A= (p×q)/2 {where p = diagonal 1 and q = diagonal 2}

Perimeter = 80 m

So, Length of a side = 80/4 = 20m

Diagonal of a rhombus = 24m,

As, we know that,

The halves of diagonals and a side of a rhombus from a right angled triangle with side as hypotenuse.

Let the length of the other diagonal =2x.

x² + (24/2)² = 20²

x² + 144 = 400

x² = 400 − 144

x² = 256

x = √256

x = 16

The measure of diagonal 2 = 2×16 = 32 m

So, Area of the rhombus = 1/2×32×24

.°. Area of the rhombus = 384m²

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