Question

find the area of a rhombus whose perimeter is 32cm,1 diagonal 10cm

Answer 1

Perimeter of Rhombus = 4 x side

32 = 4 x side
side = 32 ÷ 4 = 8 cm

Now , we know that diagonals of a rhombus bisect each other at 90° .

One of the diagonals is 10 cm.
So it's half will be 5 cm.

Using Pythagoras theorem-,
5^2 + x^2 = 8^2

Here x is the half of the second diagonal.
64 - 25 = x^2
✓39 = x.

The diagonal will be 2x = 2√39

Area = 1/2 x 1st diagonal x 2nd diagonal .
= 1/2 x 10 x 2√39 = 10√39 sq cm.

See the picture attached.

Hope This Helps You!