# NCERT Solutions for Class 9 Maths

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# Herons Formula

Exercise 1

1.    A traffic signal board, indicating ‘SCHOOLAHEAD’ is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board? 2.   The triangular side walls of a flyover has been used for advertisements. The sides of the walls are 122 m, 22 m and 120 m (see figure). The advertisement yield an earning of Rs. 5000 per mper year. A company hired one of its walls for 3 months, how much rent did it pay? 3.    There is slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN”, (see figure). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour. 4.    Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.

5.    Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.

6.   An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

Exercise 2

7.    A park, in the shape of a quadrilateral ABCD has ∠ C = 90°, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy?

8.   Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

9.   Radha made a picture of an aeroplane with coloured paper as shown in figure. Find the total area of the paper used. 10.   A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 29 cm and 30 cm and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

11.   A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, grass of how much area of grass field will each cow be getting?

12.   An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see figure), each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella? 13.   A kite is in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in figure. How much paper of each side has been used in it?

14.   A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm (see figure). Find the cost of polishing the tiles at the rate of 50 paise per cm2. 15.   A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.

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