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
45 Likes

Question

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

KnowledgeBoat · Accepted Answer

For Δ ABD, By using the Pythagoras theorem, Base² + Height² = Hypotenuse² ⇒ AB² + BD² = AD² ⇒ AB² + (24)² = (26)² ⇒ AB² + 576 = 676 ⇒ AB² = 676 - 576 ⇒ AB² = 100 ⇒ AB = ⇒ AB = 10 cm Area of Δ ABD = x AB x BD = x 10 x 24 cm² = 5 x 24 cm² = 120 cm² Area of equilateral triangle BCD = x side² = x 24² = x 576 = 144 cm² = 249.41 cm² Total area of quadrilateral ABCD = Δ ABD \+ Δ BCD = 120 \+ 249.41 cm² = 369.41 cm² Hence, the area of quadrilateral ABCD is 369.41 cm².

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.