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

For Δ ABD, By using the Pythagoras theorem, Base 2 + Height 2 = Hypotenuse 2 ⇒ AB 2 + BD 2 = AD 2 ⇒ AB 2 + (24) 2 = (26) 2 ⇒ AB 2 + 576 = 676 ⇒ AB 2 = 676 - 576 ⇒ AB 2 = 100 ⇒ AB = ⇒ AB = 10 cm Area of Δ ABD = x AB x BD = x 10 x 24 cm 2 = 5 x 24 cm 2 = 120 cm 2 Area of equilateral triangle BCD = x side 2 = x 24 2 = x 576 = 144 cm 2 = 249.41 cm 2 Total area of quadrilateral ABCD = Δ ABD \+ Δ BCD = 120 \+ 249.41 cm 2 = 369.41 cm 2 Hence, the area of quadrilateral ABCD is 369.41 cm 2 .

Find the area of a quadrilateral one of whose diagonals is 30 cm long and the perpendiculars from the other two vertices are 19 cm and 11 cm respectively.

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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 AB = 32 cm, AD = 24 cm, ∠A = 90° and BC = CD = 52 cm.

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Mathematics

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

Mensuration

Related Questions

Find the area of a quadrilateral one of whose diagonals is 30 cm long and the perpendiculars from the other two vertices are 19 cm and 11 cm respectively.

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 AB = 32 cm, AD = 24 cm, ∠A = 90° and BC = CD = 52 cm.