Area of Rhombus

Introduction In a parallelogram if all the sides are equal then it is called rhombus. Note: In a rhombus, 1. All the sides are equal 2. Opposite sides are parallel 3. Diagonal divides the rhombus into two pair of triangles with equal area. 4. The diagonal bisect each other at right angles.

Formula for finding the area of Rhombus Area of the rhombus in terms of its base and height Let the base of the rhombus be b units and its corresponding height be h units. Since a rhombus is also a parallelogram we can use the same formula to find the area of the rhombus. The area of the rhombus = b × h sq. units Area of the rhombus in terms of its diagonals Area of the rhombus = x (product of diagonals) sq. units The area of the rhombus = x d1 x d2 sq. units

When base and height are given Example 1: Find the area of a rhombus whose side is 24 cm and the altitude (height) is 14cm. When base and height are given Area of rhombus = b x h Solution: Given: Base = 24cm, Height = 14cm; To find: Area We know that rhombus is also a parallelogram, Area of Rhombus = b x h sq units = 24 x 14 = 336 cm2 Area of a Rhombus = 336 cm2

When diagonals d1 and d2 are given Example 2: Find the area of a rhombus whose diagonals are 12 cm and 20cm. Solution: Given: d1 = 12 cm, d2 = 20 cm; To find: Area When diagonals d1 and d2 are given Area of rhombus = d1 x d2 Area of Rhombus = x d1 x d2 sq units = x 12 x 20 = 12 x 10 = 120 cm2 10 Area of a Rhombus = 120 cm2

When diagonals d1 and d2 are given Example 3: Find the area of a rhombus whose diagonals are 18 cm and 24cm. Solution: Given: d1 = 18 cm, d2 = 24 cm; To find: Area When diagonals d1 and d2 are given Area of rhombus = d1 x d2 Area of Rhombus = x d1 x d2 sq units = x 18 x 24 = 18 x 12= 216 cm2 12 Area of a Rhombus = 216 cm2

Try These Find the area of a rhombus whose base is 10cm and height is 7 cm Find the area of a rhombus whose diagonals are 8 cm and 16 cm.