NCERT Solutions Class 9 Mathematics Chapter 12 Heron’s Formula Download In Pdf

Chapter 12 Heron’s Formula Download in Pdf

XERCISE 12.1

**Question
1.** 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, what will be the area of the signal board?

**Question 2.** The triangular side walls of a flyover have been used for advertisements. The sides of
the walls are 122 m, 22 m and 120 m (see Fig. 12.9). The advertisements yield an
earning of Rs 5000 per m2 per year. A company hired one of its walls for 3 months. How
much rent did it pay?

** Question 3.** There is a 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 Fig. 12.10 ). If the sides of the
wall are 15 m, 11 m and 6 m, find the area painted in colour.
Fig. 12.10

** Question 4.** Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is
42cm.

** Question 5.** Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540cm. 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 12.2

**Question 1.** A park, in the shape of a quadrilateral ABCD, has ∠ C = 90º, AB = 9 m, BC = 12 m,
CD = 5 m and AD = 8 m. How much area does it occupy?

**Question 2.** 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.

**Question 3.** Radha made a picture of an aeroplane with coloured paper as shown in Fig 12.15. Find
the total area of the paper used.

**Question 4.** A triangle and a parallelogram have the same base and the same area. If the sides of
the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base
28 cm, find the height of the parallelogram.
Fig. 12.14

**Question 5.** 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, how much area of grass field will each
cow be getting?

** Question 6.** An umbrella is made by stitching 10 triangular pieces of cloth of two different colours
(see Fig. 12.16), each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each
colour is required for the umbrella?
7. A kite 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
Fig. 12.1

**Question 7.** How much paper of each shade has been used in it?
Fig. 12.16 Fig. 12.17

**Question 8.** 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 Fig. 12.18).
Find the cost of polishing the tiles at the rate
of 50p per cm2.

**Question 9.** 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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- Chapter 3 Coordinate Geometry
- Chapter 4 Linear Equations In Two Variables
- Chapter 7 Triangles
- Chapter 8 Quadrilaterals
- Chapter 9 Areas of Parallelograms and Triangles
- Chapter 10 Circles
- Chapter 11 Constructions
- Chapter 12 Heron’s Formula
- Chapter 13 Surface Areas and Volumes
- Chapter 14 Statistics
- Chapter 15 Probability

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