Two adjacent sides of a parallelogram are 16 and 24 centimetres long. The height from the longer side is 15 centimetres. What is the height from the shorter side?

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Solution

Let ABCD be the given parallelogram with AB = DC = 24 cm, BC = AD = 16 cm and AE = 15 cm.

Construction: Draw the height AF from the shorter side AD.

We know that the area of a parallelogram is the product of the length of one side and its distance to the opposite side.

∴ Area of the parallelogram ABCD = DC × AE

= 24 cm × 15 cm

= 360 cm²

Area of parallelogram ABCD can also be written in terms of the product of the length of other side and its distance to the opposite side.

∴ Area of the parallelogram ABCD = BC × AF

⇒ 360 cm²= 16 cm × AF

Thus, the height from the shorter side is 22.5 cm.

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