Question

The area of a parallelogram is 30 square centimetres. One of its sides is 6 centimetres and one of its angles is 60°. What is the length of its other side?

Answer 1

Let ABCD be the given parallelogram.

DC = 6 cm and ∠ADC = 60°

Area of parallelogram ABCD = 30 cm²

Construction: Draw AE perpendicular to DC.

Area of a parallelogram = Base × Height

⇒ 30 cm² = 6 cm × AE

⇒ AE =

Using angle sum property in ΔAED:

∠ADE + ∠DEA + ∠EAD = 180°

⇒ 60° + 90° + ∠EAD = 180°

⇒ 150° + ∠EAD = 180°

⇒ ∠EAD = 180° − 150° = 30°

Thus, the angles of ΔAED are 30°, 60° and 90°.

Therefore, the ratio of the lengths of the sides of ΔAED is 1::2.

Thus, the length of other side of the parallelogram is cm.

Note: We can also draw the figure by taking ∠ADE = 60° and AD = 6 cm.