Question

Find the area and perimeter of a rhombus whose diagonals measure 18 cm and 24 cm.

Answer 1

Given:

• Diagonal d₁ = 18 cm
• Diagonal d₂ = 24 cm

Step-wise calculation:

1. Area of rhombus is given by:

Area = `(d_1 xx d_2)/2`

= `(18 xx 24)/2`

= `432/2`

= 216 cm²

2. To find the perimeter, first find the length of one side.

The diagonals of a rhombus bisect each other at right angles, so each half diagonal forms a right triangle with the side as the hypotenuse.

Half diagonals are:

`d_1/2 = 9  cm`

`d_2/2 = 12  cm`

Side length (a) is: 

`a = sqrt((d_1/2)^2 + (d_2/2)^2`

= `sqrt(9^2 + 12^2)`

= `sqrt(81 + 144)`

= `sqrt(225)`

= 15 cm

3. The perimeter of rhombus is:

Perimeter = 4 × a

= 4 × 15

= 60 cm

Area of the rhombus = 216 cm².

Perimeter of the rhombus = 60 cm.