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

In right-angled △ABC, Using Pythagoras theorem, ⇒ AB 2 = AC 2 + BC 2 Substituting the values we get, ⇒ 13 2 = 12 2 + BC 2 ⇒ BC 2 = 13 2 – 12 2 ⇒ BC 2 = 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 cm 2 + 62.35 cm 2 = 92.35 cm 2 . Hence, area of quadrilateral ABCD = 92.35 cm 2 .

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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

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