Question

A rohmbus one of the diagnol 20cm
perimeter of the rohmbus 104cm
find the area.​

Answer 1

Answer:

480 cm²

Step-by-step explanation:

One diagonal of rhombus = 20 cm.

Perimeter = 104 cm.

Formula for perimeter of rhombus = 4 * Side

4 * Side = 104

=> Side = 104/4 = 26 cm.

In a rhombus the diagonals bisect each other at O.

=> AO = 20/2 = 10 cm. DO = BD/2.

So using Pythagoras theorem, calculate the

AD² = AO² + OD²

26² = 10² + OD²

OD = √676 - 100 = 576 = 24.

Thus full length of other diagonal = 2 * 24 = 48 cm.

Now area of rhombus = 1/2 * d₁ * d₂ = 1/2 * 20*48 = 480 cm²