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Heron's Formula
Submitted by: Gagan Chaudhary (Haryana)
Assignment 1
1. The lengths of the sides of a triangle are in the ratio 3:4:5 and its perimeter is 144 cm. Find (i) area of triangle, (ii) height corresponding to the longest side.
2. Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD = 9 cm, CD = 12 cm, ACB = 90 and AC = 15 cm.
3. The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm and the diagonal AC measures 42 cm. Find the area of the parallelogram.
4. A rectangular lawn, 75 m by 60 m has two roads, each 4 m, running through the middle of the lawn, one parallel to the length and other parallel to the breadth. Find the cost of gravelling the roads at Rs.4.50 per m2.
5. Find the area of a trapezium whose parallel sides are 11 m and 25 m and the non parallel sides are 15 m and 13 m long.
6. The difference between the lengths of parallel sides of a trapezium is 8 cm. and the perpendicular distance between these sides is 24 cm and the area of trapezium is 312 cm2. Find the length of each of the parallel sides.
7. Using Heron's Formula, find the area of an equilateral triangle whose one side measures a cm. Using that formula, find area of an equilateral triangle, whose one side measures 6 cm.
ANSWERS
1.864 cm2, 28.8 cm 2. 46cm, 114 cm2 3. 672 cm2
4. Rs.2358 5. 216 m2 6. 17 cm, 9 cm 7. /3 a2, 9/3 cm2
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