*NCERT Solutions of Chapter: Heron’s Formula . NCERT Solutions along with worksheets and notes for Class 9.*

**Exercise 12.1**

**(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 f the signal board?**

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**(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 (Figure below). The advertisements yield an earning of Rs 5000 per m ^{2} per year. A company hired one of its walls for 3 months. How much rent did it pay?**

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**(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”(Figure below). If the sides of eh wall are 15 m, 11m and 6 m, find the area painted in colour.**

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

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

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

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

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**(3)** **Radha made a picture of an areoplane with coloured paper as shown in figure below. Find the total area of the paper used.**

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**In figure III**

**(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.**

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**(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?**

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**(6) An umbrella made by stitching 10 triangular pieces of cloth of two different colours (Figure below), each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?**

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**(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 figure below. How much paper of each shade has been used in it?**

**Ans-**

**(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 (figure below). Find the cost of polishing the titles at the rate of 50 p per cm ^{2}.**

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**(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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**I ^{st }Method (Using Heron’s Formula)**

**II ^{nd} Method (Without using Heron’s Formula**

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**Helping Topics**