Question

find the area of a rhombus whose side is 6.5cm and altitude is 5cm.If one of its diagonal is 13 cm long, find the length of other diagonal.

Answer 1

I hope I am not wrong

Answer 2

Answer:

Area of rhombus = 32.5 cm²

The length of other diagonal = 5 cm.

Explanation:

As per the question,

Base = 6.5 cm

Height = 5cm

d₁ = 13 cm

First draw a rhombus as per the question, which is drawn below

Now,

Area of rhombus PQRS = Area of Δ PQR + Area of Δ PSR

And

Area of Δ PQR = $\frac{1}{2}\times base\times height$

                        =  $\frac{1}{2}\times 6.5\times 13$

                        = 16.25 cm²

Similarly,

Area of Δ PSR = $\frac{1}{2}\times base\times height$

                        =  $\frac{1}{2}\times 6.5\times 13$

                        = 16.25 cm²

∴ Area of rhombus PQRS = 16.25 + 16.25 = 32.5 cm²

As we know,

Area of rhombus is also given by

$Area=\frac{1}{2}\times d_{1}\times d_{2}$

Or

$32.5=\frac{1}{2}\times 13\times d_{2}$

$32.5 \times 2= 13\times d_{2}$

d₂ = 5 cm

Hence, the length of other diagonal = 5 cm.