Question

6. Find the area of a rhombus whose perimeter is 60 cm
and one diagonal is of length 18 cm.
​

Answer 1

Answer:

Area = 100√5 cm²

Explanation:

Given

• Perimeter = 60cm

• Length of diagonal = 18 cm

To find :

• Area of rhombus = ?

Procedure :

Let's consider rhombus ABCD

Perimeter of ABCD = 60cm

Let sides of rhombus, AB = BC = CD = DA = x

$Perimeter = x + x + x + x$

$\implies \sf \: 60 = 4x$

$\implies \sf \: x = \frac{60}{4}$

$\implies \sf \: x = 15cm$

All sides of rhombus ABCD are of 15 cm.

In ∆ ABCD

AB = AD = 15 cm

BD = 20 cm

$\sf \: Semi - perimeter = \frac{15 + 15 + 20}{2}$

$\sf \: Semi - perimeter = \frac{50}{2}$

$\sf \: Semi - perimeter =25cm$

$\rightarrow \sf \: area \: = \sqrt{s(s - a)(s - b)(s - c) \: }$

$\rightarrow \sf \: area \: = \sqrt{25(25 - 15)(25 - 15)(25 - 20) \: }$

$\rightarrow \sf \: area \: = \sqrt{25 \times 10 \times 10 \times 5 \: }$

$\rightarrow \sf \: area \: = \sqrt{5 \times 5 \times 10 \times 10 \times 5 \: }$

$\rightarrow \sf \: area \: = 50 \sqrt{5} \: {cm}^{2}$

$\sf \: Area of ABCD = 2 \times 50 \sqrt{5}$

$\sf \: area \: of \: ABCD = 100 \sqrt{5} \: cm^{2}$