Compute the perimeter of the quadrilateral with measures as given below, correct to centimetres:

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Solution

In ΔADC, using Pythagoras theorem, we have:

In ΔABC, ∠BAC =∠BCA = 60°

Using angle sum property:

∠ABC + ∠BCA + ∠BAC = 180°

⇒ ∠ABC + 60° + 60° = 180°

⇒ ∠ABC = 180° − 120° = 60°

Therefore, ΔABC is an equilateral triangle.

⇒ AB = BC = CA ≈ 1.41 m

We know that perimeter of a quadrilateral is equal to the sum of lengths of all its sides.

∴ Perimeter of quadrilateral ABCD ≈ (1 + 1 + 1.41 + 1.41) m = 4.82 m

Thus, the perimeter of the given quadrilateral is approximately equal to 4.82 m.

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