Here we will discuss about *how to find the area of a parallelogram*. To calculate area of parallelogram we need to remember the formula and solve step-by-step.

ABCD is a parallelogram with base (b) and altitude (h).

*Area of parallelogram = 2 × Area of ∆ABC *

= 2 × 1/2 × base × height sq. units

= 2 × 1/2 × AB × CE sq. units

= b × h sq. units

= base × height sq. units

*Perimeter of parallelogram = 2(AB + BC)*

= 2 × (Sum of adjacent sides)

**Worked-out examples on area of parallelograms:**

**1. ** The base of the parallelogram is thrice its height. If the area is 192 cm², find the base and height.

**Solution:**

Let the height of the parallelogram = x cm

then the base of the parallelogram = 3x cm

Area of the parallelogram = 192 cm²

Area of parallelogram = base × height

192 = 3x × x

⇒ 3x² = 192

⇒ x² = 64

⇒ x = 8

Therefore, 3x = 3 × 8 = 24

Therefore, Base of the parallelogram is 24 cm and height is 8 cm.

**2. ** A parallelogram has sides 12 cm and 9 cm. If the distance between its shorter sides is 8 cm, find the distance between its longer side.

**Solution:**

Adjacent sides of parallelogram = 2 cm and 9 cm

Distance between shorter sides = 8 cm

Area of parallelogram = b × h

= 9 × 8 cm²

= 72 cm²

Again, area of parallelogram = b × h

⇒ 72 = 12 × h

⇒ h = 72/12

⇒ h = 6 cm

Therefore, the distance between its longer side = 6 cm.

**3. ** ABCD is a parallelogram in which AB = 20 cm, BC = 13 cm, AC = 21 cm. Find the area of parallelogram ABCD.

**Solution:**

Area of parallelogram ABCD = 2 area of ∆ABC

In ∆ ABC,

AB = 20 cm BC = 13 cm AC = 21 cm

So, s = (20 + 15 + 21)/2

= 54/2

= 27

Therefore, area of ∆ABC = √(27 (27 - 20) (27 - 13) (27 - 21))

= √(27 × 7 × 14 × 6)

= √(3 × 3 × 3 × 7 × 2 × 7 × 2 × 3)

= 2 × 3 × 3 × 7

= 126 cm²

Area of parallelogram ABCD = 2 area of ∆ABC

= 2 × 126 cm²

= 252 cm²

The detailed explanations on the formula of perimeter and area of parallelogram are explained above with the step-by-step solution.

**● Mensuration**

**Perimeter and Area of Rectangle**

**Area and Perimeter of the Triangle**

**Area and Perimeter of the Parallelogram**

**Circumference and Area of Circle**

**Practice Test on Area and Perimeter of Rectangle**

**Practice Test on Area and Perimeter of Square**

**● Mensuration - Worksheets**

**Worksheet on Area and Perimeter of Rectangles**

**Worksheet on Area and Perimeter of Squares**

**Worksheet on Circumference and Area of Circle**

**Worksheet on Area and Perimeter of Triangle**

**7th Grade Math Problems** **8th Grade Math Practice** **From Area of Parallelogram to HOME PAGE**

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