Calculate the area of quadrilateral ABCD in which AB = 32 cm, AD = 24 cm, ∠A = 90° and BC = CD = 52 cm.

Quadrilateral ABCD is shown in the figure below: Area of Δ DAB = x base x height = x DA x AB = x 24 x 32 cm 2 = 12 x 32 cm 2 = 384 cm 2 By using the Pythagoras theorem, AD 2 \+ AB 2 = BD 2 ⇒ 24 2 + 32 2 = BD 2 ⇒ 576 + 1,024 = BD 2 ⇒ 1,600 = BD 2 ⇒ BD = ⇒ BD = 40 cm In triangle BCD, Let the sides of the triangle be: a = 40 cm, b = 52 cm and c = 52 cm. The semi-perimeter s: ∵ Area of Δ BCD = = cm 2 = cm 2 = cm 2 = 960 cm 2 Therefore, area of quadrilateral ABCD = Area of Δ DAB \+ Area of triangle BCD = 384 \+ 960 cm 2 = 1344 cm 2 Hence, the area of quadrilateral ABCD is 1344 cm 2 .

The diagonals of a quadrilateral are 16 cm and 13 cm. If they intersect each other at right angles; find the area of the quadrilateral.

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Calculate the area of quadrilateral ABCD, in which ∠ABD = 90°, triangle BCD is an equilateral triangle of side 24 cm and AD = 26 cm.

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Mathematics

Calculate the area of quadrilateral ABCD in which AB = 32 cm, AD = 24 cm, ∠A = 90° and BC = CD = 52 cm.

Mensuration

Related Questions

The diagonals of a quadrilateral are 16 cm and 13 cm. If they intersect each other at right angles; find the area of the quadrilateral.

Calculate the area of quadrilateral ABCD, in which ∠ABD = 90°, triangle BCD is an equilateral triangle of side 24 cm and AD = 26 cm.

A rectangular plot 85 m long and 60 m broad is to be covered with grass leaving 5 m all around. Find the area to be laid with grass.