Question

calculate the area and perimeter of a rhombus PQRS where PR=10 , QS=24 ​

Answer 1

Answer:

Area = 120, Perimeter = 52

Step-by-step explanation:

Diagonal PR = 10

Diagonal QS = 24

Area of a Rhombus = d1 x d2 / 2

                                = 10 x 24 / 2

                                = 120

Area of Rhombus PQRS is 120.

Perimeter = 4a where a is the length of a side.

We have to find the length of a side.

The diagonals divides the Rhombus into 4 triangles.

Let's take a triangle and find the base of it.

Let a be base, b and c be the half of the diagonals.

b = 10 / 2 = 5

c = 24 / 2 = 12

Using Pythagoras Theorem,

5² + 12² = a²

a² = 25 + 144

a² = 169

a = 13

∴ Length of a side = 13

Perimeter = 4a

                 = 4 x 13

                 = 52

∴Perimeter = 52