# The Height of a Parallelogram Is One Third of Its Base. Area of the Parallelogram Is 192cm2

## Question: The height of a parallelogram is one-third of its base. If the area of the parallelogram is 192 cm^{2}, find its height and base.

A parallelogram is defined as a quadrilateral in which both pairs of opposite sides are parallel and equal.

## Answer:

Let's explore more about the properties of parallelograms and the area of parallelograms.

## Explanation:

The area of a parallelogram is base × height.

Given that the height of the parallelogram is 1/3 of its base.

⇒ h = 1/3 of b

⇒ b = 3h

Area of the parallelogram = 192 cm^{2}

⇒ b × h = 192

⇒ 3h × h = 192

⇒ 3h^{2} = 192

⇒ h^{2} = 192/3

⇒ h^{2} = 64

⇒ h = 8 cm

⇒ b = 3h = 3(8) = 24 cm

### Thus, the height and base of the given parallelogram are 8 cm and 24 cm respectively.

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