Find the area of the quadrilateral ABCD in which ∠BCA = 90°, AB = 13 cm and ACD is an equilateral triangle of side 12 cm.
Mensuration
146 Likes

Question

Find the area of the quadrilateral ABCD in which ∠BCA = 90°, AB = 13 cm and ACD is an equilateral triangle of side 12 cm.

KnowledgeBoat · Accepted Answer

In right-angled △ABC, Using Pythagoras theorem, ⇒ AB² = AC² + BC² Substituting the values we get, ⇒ 13² = 12² + BC² ⇒ BC² = 13² – 12² ⇒ BC² = 169 – 144 = 25 ⇒ BC = = 5 cm. Calculating area of △BCA, Calculating area of △ACD, From figure, Area of quadrilateral ABCD = Area of △BCA + Area of △ACD = 30 cm² + 62.35 cm² = 92.35 cm². Hence, area of quadrilateral ABCD = 92.35 cm².

Mathematics

Find the area of the quadrilateral ABCD in which ∠BCA = 90°, AB = 13 cm and ACD is an equilateral triangle of side 12 cm.

Mensuration

Related Questions

Find the area of a quadrilateral whose diagonals are of length 18 cm and 12 cm and they intersect each other at right angles.

Find the area of the quadrilateral field ABCD whose sides AB = 40 m, BC = 28 m, CD = 15 m, AD = 9 m and ∠A = 90°.

Find the area of quadrilateral ABCD in which ∠B = 90° , AB = 6 cm, BC = 8 cm and CD = AD = 13 cm.

The perimeter of a rectangular cardboard is 96 cm; if its breadth is 18 cm, find the length and the area of the cardboard.