Heron FormulaAll Questions carries one mark each.1. The base and hypotenuse of a right triangle are respectively 12 cm and 20 cm long its area is (a) 96 cm2 (b) 120 cm2 (c) 135 cm2 (d) 140 cm2 2. If every side of a triangle is doubled, then increase in area of the triangle is (a) 200% (b) 100% (c) 300% (d) 400% 3. The sides of a triangle are 16 cm, 20 cm and 24 cm. Its area is

(a) 40cm2 (b) 60cm2 (c) 50cm2 (d) 80cm2

4. The side of an isosceles right triangle of hypotenuse 7 cm is (a) 6 cm (b) 7 cm (c) 5 cm (d) 8 cm 5. The length of each side of an equilateral triangle of area 9I cm2, is (a) 4 cm (b) 6 cm (c) 5 cm (d) 7 cm 6. The sides of a triangle are 25 cm, 39 cm and 56 cm. The area of the triangle is (a) 210 cm2 (b) 420 cm2 (c) 840 cm2 (d) 1680 cm2 7. The sides of a triangle are 8 cm, 11 cm and 13 cm. The altitude of the smallest side is

(a) cm (b) 3cm (c) 4 cm (d) 5cm 8. The base and hypotenuse of a right triangle are respectively 15 cm and 25 cm. Its area is (a) 120 cm2 (b) 135 cm2 (c) 150 cm2 (d) 145 cm2 9. The sides of a triangle are 9 cm. 28 cm (a) 30,k; cm2 (c) 36,/ cm2 (b) 32,/6 cm2 (d) 35,1,3 cm210. If the altitude of an equilateral triangle and 35 cm. Its area is is 315 cm, then its area is equal to(a) 64 cm2 (c) 9,h cm2 (b) cm2 (d) 1213- cm2 11. If the altitude of an equilateral triangle is 5 cm, then its area is equal to (a) 25 cm225 /7, 2 (b) .5 cm 2 25(c) 252 (d) 2 12. The sides of a triangle are 50 cm, 78 cm and 112 cm. The area of the triangle is (a) 840 cm2 (b) 1680 cm2 (c) 420 cm2 (d) 3360 cm2 13. The sides of a triangle are 11 cm, 15 cm and 16 cm. The area of the triangle is (a) 30 cm2 (b) 30-J7 cm2 (c) 60.1i cm2 (d) 15-J1 cm2 14. A square and an equilateral triangle have equal perimeters. If the diagonal of the square is cm, then area of the triangle is (a) 36/ (b) 36h cm2 (c) 2413- cm2 (d) 48-IS cm2 15. If two sides of a triangle are 8 cm, 11 cm and the perimeter is 32 cm, then the area of triangle is (a) 9,/k1 cm2 (b) 4-JTO cm2 (c) 8,/5 cm2 (d) 6jd cm2 16. The length of each side of an equilateral triangle of area 9../ cm2, is (a) 3 cm (b) 6 cm (c) 9 cm (d) 4.5 cm 17. The sides of an isosceles right triangle of hypotenuse 4,rf cm is (a) 6 cm (b) 8 cm (c) 4 cm (d) 4 cm 18. The sides of a triangle are 16 cm, 30 cm, 34 cm. Its area is (a) 250 cm2 (b) 280 em2 (c) 220 cm2 (d) 240 cm2 19. The sides of a triangle are 11 m, 60 m and 61 m. The area of the triangle is 660 m2. (a) 660 m2 (b) 330 m2 (c) 220 m2 (d) 440 m2 20. If the area of an isosceles right triangle is 8 cm2, then the perimeter of the triangle is

(a) (8 +) cm (b) (8 + 4) cm (c) (4 + 8) cm(d) 12 cm

Answers:-1. (a) 2. (c) 3. (b) 4. (b)5. (b) 6. (b)7. (a) 8. (c)9. (c) 10. (b) 11. (c) 12. (b) 13. (b)14. (a)15. (c) 16. (b) 17. (d) 18. (d) 19. (b) 20. (b)

All Questions carries three mark each.1. If the angles of a triangle are in the ratio 2 : 3 : 4, find the angles of the triangle. OrShow that the angles of an equilateral triangle are 600 each. 2. Students of a school staged a rally for cleanliness campaign. They walked through the lanes in two groups. One group walked through the lanes AB, BC and CA; while the other through AC, CD and DA (see figure). Then they cleaned the area enclosed within their lanes. If AB = 9 m, BC = 40 m, CD = 15 m, DA = 28 m and LB = 90, which group cleaned more area and by how much? Find the total area cleaned by the students (neglecting the width of the lanes).

3. Two triangular walls of a flyover has been used for advertisement. The sides of each wall are 100m, 80m & 40m. The advertisement yields an earning of 1200 per m2 per year. Find the amount of revenue earned in one year. [Take = 15.2] 4. A traffic signal board, indicating 'SCHOOL AHEAD' is an equilateral triangle with side 'a'. Find the area of the signal board, using Heron's formula, if its perimeter is 180 cm.5. Find the area of a triangle, two sides of which are 18 cm and 10 cm and the perimeter is 42 cm. 6. In figure

7. A triangular park in a city has dimensions 30 m x 26 m x 28 m. A gardener has to plant grass inside the park at 1.50 per m2. Find the amount to be paid to the gardener. 8. Sides of a triangle are in the ratio of 12: 17 : 25 and its perimeter is 540 cm. Find its area. 9. The lengths of the sides of a triangle are in the ratio and its perimeter is area of the triangle using Heron's formula. 10. The lengths of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. Find the area of the triangle. 11. An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

Answers: -1. 400, 60, 802. Area of ACD = 126 m2. First group cleaned 54 m2 more area cleaned by the second group. Total area cleaned by all the students = 306 m2.

3. 1520 m2 and total revenue = ` 3,648,000 4. Area = 900 cm2 5. 21 'II cm26. 20../2 m27. 5048. Area of A = 9000 cm2 9. Area of A = 864 cm2 10. 864 cm211. 9 cm2