Question

Find the area of a rhombus whose side is 20cm and altitude is 6cm. If one of its diagonals is 24cm long, find the length of the other diagonal.

Answer 1

Rhombus is also a parallelogram,
So, Area of Rhombus = base*height
                                    = 20*6
                                    = 120 cm²

We also know that, Area of Rhombus = product of diagonals/2
                     So, 120 = 24 * other diagonal/2
               so, Length of other diagonal = 10 cm

Answer 2

we know that diagonal of a rhombus divides it into two congruent triangles with equal area
so are of triangle 1=1/2 bh
=20×6/2=60cm^2
similarly are of triangle 2 =60cm^2
so are of rhombus=are of triangle 1 + are of triangle 2=120cm^2
area of rhombus=d1d2/2
120=24×d2
d2=120/24
d2=5cm