herons formula

Heron’s formula

Introduction to heron’s formula

Introduction of another formula for area of a triangle

• Most of us are aware with : • Area of a triangle = Where b = base and h = corresponding height

of the triangle

Examples :

• 1) Find the area of a triangle having sides : AB = 4 cm BC = 3 cm CD = 5 cm

Solution of Example 1)

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Example 2:

2) Rahul has a garden, which is triangular in shape. The sides of the garden are 13 m, 14 m, and 15 m respectively. He wants to spread fertilizer in the garden and the total cost required for doing it is Rs 10 per m2. He is wondering how much money will be required to spread the fertilizer in the garden

Solution of Example 2)

• Given a = 13 m , b = 14 m and c = 15 m

So , we will find the area of the triangle by using Heron’s formula.

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21(21 13)(21 14)(21 15) 21*8*7*6=

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• Given the rate = Rs 10 per m^2 • Now :

• Total cost = Rs. 10 * 84 = Rs 840/-

Area of a quadrilateral

• Suppose there is a quadrilateral having sides : a , b , c and d and diagonal r.

The diagonal d divides the quadrilateral into 2 triangles.

So : Ar(ABCD)= Ar(ABD) + Ar(BCD)

Continued

1) Area of triangle : ABD Heron’s formula: Putting the values we get :

Continued..

Solution of exampleAs we have the formula written below for the area of a quadrilateral

Where : a = 4cm b = 3 cm c = 5 cm d = 6 cmAnd r (diagonal ) = 7 cm

cm2

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How to find the area of an equilateral triangle

Concept based question

• What equilateral triangle would have the same area as a triangle with sides 6, 8 and 10?

Solution

• First of all we will find the area of the triangle having sides : a = 6 units , b = 8 units and c = 10 units