Question

the perimeter of a rhombus is 40 cm if one of its diagonal is 16 cm find the area of the Rhombus

Answer 1

let the length of each side of rhombus be a.
perimeter of rhombus= 40 cm.
a+a+a+a=40
4a=40
a=10cm
it's one diagonal is 16 cm.
since ,diagonal of rhombus intersect each other at right angles.
length of other diagonal will be:
length of other diagonal= 2(10²-8²)=2×6=12 cm.
and we also know that:
area of rhombus= 1/2×d1×d2.
=1/2×12×16=12×8=96cm². answer

Answer 2

Given - Perimeter of rhombus = 40 cm

One diagonal = 16 cm

Find - Area of rhombus

Solution - Formula for area of rhombus = 1/2*diagonal1*diagonal2

Firstly calculating value of second diagonal.

The formula is -

side² = (diagonal1/2)² + (diagonal2/2)²

Calculating side of the rhombus.

Perimeter = 4*side

40 = 4*side

side = 10 centimetres

Calculating value of diagonal 2 now.

10² = (16/2)² + (diagonal2/2)²

100 = 8² + (diagonal2/2)²

100 = 64 + (diagonal2/2)²

(diagonal2/2)² = 100 - 64

(diagonal2/2)² = 36

Diagonal2/2 = ✓36

Diagonal2/2 = 6 centimetres

Diagonal2 = 12 centimetres.

Now, calculating area of rhombus.

Area of rhombus = 1/2*16*12

Area of rhombus = 8*12

Area of rhombus = 96 cm²

Thus, area of rhombus is 96 cm²