# Area of Rhombus

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As all the sides of rhombus are equal so the perimeter of rhombus is same as that of square.

**The diagonals of rhombus bisect each other at right angle.**

**•**Perimeter of Rhombus = 4 x side

**•**Area of a rhombus = ½ [ product of the diagonals]

**•**Area = Base x Height

**Some solved examples :**

1) The side of a rhombus is 18 cm . Find its perimeter.

**Solution :**

Perimeter of Rhombus = 4 x side

⇒ = 4 x 18

&rArr = 72 cm

∴ Perimeter of Rhombus = 72 cm.

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2) Find the area of a rhombus having each side equal to 13 cm and one of whose diagonal is 24 cm.

**Solution :**

Let ABCD is a rhombus with diagonals AC and BD which intersect each other at O.

AC = 24 ⇒ AO = 12

Let BO = x and AB = 13 cm (given)

By Pythagorean theorem

c

^{2}= a

^{2}+ b

^{2}

13

^{2}= 12

^{2}+ x

^{2}169 = 144 + x

^{2}

x

^{2}= 169 – 144

x

^{2}= 25

x = 5 cm

BO = 5 cm

Diagonal BD = 2 x 5 = 10 cm.

Area = ½ x [ product of diagonals]

= ½ x 24 x 10

Area = 120 sq.cm

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3) If the area of a rhombus is 24 sq.cm and one of its diagonal is 4 cm find the length of the other diagonal.

**Solution :**

Area = ½ x d1 x d2

24 = ½ x 4 x d2

24 = 2 x d2

d2 = 24/2

d2 = 12 cm

**Mensuration : Area and Perimeter**

• Perimeter and Area of Irregular Shape

• Area and Perimeter of the Rectangle

• Area of Square (perimeter of square)

• Perimeter of Parallelogram(Area of Parallelogram)

• Area of Rhombus(Perimeter of rhombus)

• Area of Trapezoid (Trapezium)

• Triangle Area (Perimeter of triangle)

• Herons Formula

• Perimeter and Area of Irregular Shape

• Area and Perimeter of the Rectangle

• Area of Square (perimeter of square)

• Perimeter of Parallelogram(Area of Parallelogram)

• Area of Rhombus(Perimeter of rhombus)

• Area of Trapezoid (Trapezium)

• Triangle Area (Perimeter of triangle)

• Herons Formula

7th grade math

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