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### Grade 7 - Mathematics9.27 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.
 Q 1: In a quadrilateral ABCD, diagonal AC = 12cm. The length of perpendicular from C to AC is 8cm. Find the length of the perpendicular from B to AC if the area of the quadrilateral is given by 90 sq.cm.8 cm7 cm8 cm12 m Q 2: In a quadrilateral ABCD, diagonal AC = 15 cm. The lengths of perpendiculars from B and C to AC are 6 cm and 7 cm respectively. Find the area of the quadrilateral.97.5 sq.cm87.5 sq.cm87 sq.cm97 sq.cm Q 3: In a quadrilateral ABCD, diagonal AC = 13 cm. The length of perpendicular from C to AC is 9 cm. Find the length of the perpendicular from B to AC if the area of the quadrilateral is given by 130 sq.cm.9 cm14 cm11 cm13 cm Q 4: In a quadrilateral ABCD, diagonal AC = 11cm. The length of perpendicular from B to AC is 7cm. Find the length of the perpendicular from C to AC if the area of the quadrilateral is given by 88 sq.cm.7 cm9 cm8 cm6 cm Q 5: In a quadrilateral ABCD, the lengths of perpendiculars from B and C to AC are 6 cm and 5 cm respectively. Find the length of the diagonal if the area of the quadrilateral is given by 49.5 sq.cm.4 cm9 cm3 cm3 cm Q 6: In a quadrilateral ABCD, the lengths of perpendiculars from B and C to AC are 5 cm and 6 cm respectively. Find the length of the diagonal if the area of the quadrilateral is given by 49.5 sq.cm.9 cm3 cm6 cm4 cm Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!

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