NCERT Class 9 Solutions: Heron's Formula (Chapter 12) Exercise 12.2 Part 5

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Image gives herons formula in simple terms

Herons Forumla in Simple Terms

Image gives herons formula in simple terms

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Art derived from Herons Formula

Herons Formula Illustration

Art derived from Herons Formula

Q-8 A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being (see Fig). Find the cost of polishing the tiles at the rate of

a Floral Design Made of Triangles

A floral design is made with 16 triangular tiles

Solution:

  • Semi perimeter of each of the triangular shapes

  • Therefore, area of each of the triangular tiles

  • Therefore, total area of

  • Cost of polishing tiles =

  • Therefore, total cost of polishing tiles

Q-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.

Solution:

SBQP Is the Required Trapezium

SBQP is the trapezium with parallel sides SB=25mandPQ=10mand the non-parallel sides SP=13mandBQ=14m.

Given,

SBQP be the trapezium with parallel sides and the non-parallel sides

Construction,

  • Draw

  • Draw , therefore QPSR is now a parallelogram

In ,

  • and

  • .

  • Therefore, semi perimeter of the

Therefore, by Herons formula, area of the

Area of the parallelogram

Therefore, area of the trapezium

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