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#### Online Quiz (WorksheetABCD)

Questions Per Quiz = 2 4 6 8 10

### Geometry4.2 Area of Quadrilateral - I

 Example: In a quadrilateral ABCD, diagonal AC = 10 cm. The lengths of perpendiculars from B and C to AC are 6 cm and 7 cm respectively. Find the area of the quadrilateral. Solution: The area of a quadrilateral ABCD = 1/2 * d(h1+h2). Given that, d = 10 cm, h1 = 6 cm and h2 = 7 cm. So required area = 1/2 * 10 (6+7) = 1/2 * 10 * 13 = 5 * 13 = 65 sq.cm. Example: In a quadrilateral ABCD, the lengths of perpendiculars from B and C to AC are 6 cm and 4 cm respectively. Find the length of the diagonal if the area of the quadrilateral is given by 65 sq.cm. Solution: Let the length of the diagonal be 'x'. The area of a quadrilateral ABCD = 1/2 * d(h1+h2). Given that, h1 = 6 cm and h2 = 4 cm. i.e 65 = 1/2 * x (6+4), i.e 65 = 1/2 * x * 10, i.e 65 x 2 = 10x, i.e x = 130/10 = 13 cm. Hence the length of the diagonal is 13 cm. Directions: Read the above example carefully and answer the following questions: In a quadrilateral ABCD, the lengths of perpendiculars from B and C to AC are 15.5 cm and 12.3 cm respectively. Find the length of the diagonal if the area of the quadrilateral is given by 472.6 sq.cm.