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°.

From figure, ABCD is a quadrilateral field. In triangle BAD, ∠A = 90° Using the Pythagoras Theorem ⇒ BD 2 = AB 2 + AD 2 Substituting the values we get, ⇒ BD 2 = 40 2 + 9 2 ⇒ BD 2 = 1600 + 81 = 1681 ⇒ BD = = 41 m We know that, Area of quadrilateral ABCD = Area of △BAD + Area of △BDC Calculating area of △BDC, In △BDC, Let a = BD = 41 m, b = BC = 28 m and c = CD = 15 m. Semi-perimeter (s) = = 42 m. By Heron's formula, Area of triangle = Substituting values we get, Calculating area of △BAD, Area of quadrilateral ABCD = Area of △BAD + Area of △BDC = 180 + 126 = 306 m 2 . Hence, area of quadrilateral ABCD = 306 m 2 .

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Mathematics

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°.

Mensuration

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