Question

The perimeter of a rhombus is 100 cm and one of its diagonal is 40 cm.

Answer 1

Answer:

Area of Rhombus = 600 cm²

Step-by-step explanation:

ABCD is a rhombus.

In a Rhombus all the sides are of equal length. The diagonals of a rhombus are perpendicular and bisect each other.

Perimeter of a rhombus = 100 cm.

Thus the side of rhombus = 100/4 = 25 cm.

One of its diagonal AC = 40 cm.

=> AO = 20 cm.

ΔAOB is a right angled triangle.

Using Pythagoras theorem,

AO² + OB² = AB²

OB² = AB² - AO² = 25² - 20² = 225

OB = 15 cm.

Thus the length of other diagonal BD = 2*15 = 30 cm.

Area of Rhombus = 1/2 * Product of the Diagonals

                             = 1/2 * 30*40 = 600 cm².