heronâ€™s formula. introduction to heronâ€™s formula

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• Slide 1
• Herons formula
• Slide 2
• Slide 3
• Introduction to herons formula
• Slide 4
• 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
• Slide 5
• Examples : 1) Find the area of a triangle having sides : AB = 4 cm BC = 3 cm CD = 5 cm
• Slide 6
• Solution of Example 1)
• Slide 7
• Continue
• Slide 8
• 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 m 2. He is wondering how much money will be required to spread the fertilizer in the garden
• Slide 9
• 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 Herons formula.
• Slide 10
• Continue..
• Slide 11
• Continue Given the rate = Rs 10 per m^ 2 Now : Total cost = Rs. 10 * 84 = Rs 840/-
• Slide 12
• 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)
• Slide 13
• Continued 1)Area of triangle : ABD Herons formula: Putting the values we get :
• Slide 14
• Continued..
• Slide 15
• Slide 16
• Solution of example As we have the formula written below for the area of a quadrilateral Where : a = 4cm b = 3 cm c = 5 cm d = 6 cm And r (diagonal ) = 7 cm
• Slide 17
• cm 2 Click on this arrow to continue
• Slide 18
• How to find the area of an equilateral triangle
• Slide 19
• Concept based question What equilateral triangle would have the same area as a triangle with sides 6, 8 and 10?
• Slide 20
• Solution First of all we will find the area of the triangle having sides : a = 6 units, b = 8 units and c = 10 units
• Slide 21
• Slide 22