Question

If the perimeter of a rhombus is 68 cm and one of its diagonals is 30 cm, find its area.

Answer 1

Given:

• Perimeter of rhombus = 68 cm
• One diagonal = 30 cm
• Find: Area of the rhombus

Step-wise calculation:

1. Calculate the length of one side of the rhombus:

Side = `"Perimeter"/4`

= `68/4`

= 17 cm

2. Let the other diagonal be d₂. 

The diagonals of a rhombus bisect each other at right angles.

Each half of the diagonals forms right triangles with the side as hypotenuse.

3. Half of the given diagonal is `30/2` = 15 cm.

4. Using Pythagoras theorem in one right triangle formed by half diagonals and the side:

`(d_2/2)^2 + 15^2 = 17^2`

`(d_2/2)^2 = 17^2 - 15^2`

= 289 – 225

= 64

`d_2/2 = 8`

⇒ d₂ = 16 cm

5. Area of the rhombus is given by:

`"Area" = 1/2 xx d_1 xx d_2`

= `1/2 xx 30 xx 16`

= 240 cm²

The area of the rhombus is 240 cm².