Question

One side of rhombus is 10 cm and one of its diagonal is 12cm the area of rhombus

Answer 1

The diagonals in a rhombus are perpendicular , and bisect each other

Given length of side is 10 cm and one diagonal as 12 cm we can find the length of other diagonal

From the  above figure let DB be the 12 cm diagonal,now OB and OD are 6 cm

Now consider triangle AOB ,this is a right andled triangle and we know AB=10cm and OB=6cm ,using Pythagoras theorem we can find out lenth of OA as 8cm ,so length of diagonal AC is 2*8=16cm

Area of rhombus is product of diagonal divided  by 2, 16*12/2=96sq.cm

Answer 2

Solution:-

let, Rhombus ABCD.

given:-

•The sides of a rhombus are 10cm and one diagonal is 12 cm .

let, DO = OB = ? , BD = ?

and AO = OC = 6cm, and AC = 12 cm

1) we know diagonal of rhombus are equally bisect each other and they are perpendicular to each other.

2) All sides of rhombus are equal.

so,

by Pythagoras theorem.

=> (AB)² = ( AO )² + ( OB )²

=> (10)² = (6)² + (OB)²

=> 100 = 36 + (OB)²

=> 100 - 36 = (OB)²

=> 64 = (OB)²

i.e.

=> (OB)² = 64

=> OB = √64

=> OB = 8 cm

so, we know

DO = OB = 8 cm

hence, BD = 16 cm

Area of rhombus = [(AC)×(BD)]/2

Area of rhombus = [ 12 × 16 ]/2

Area of rhombus = [192]/2

Area of rhombus= 96 cm²

Hence length of diagonal rhombus

is 16 cm and area of rhombus is

96 cm².