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Heron’s Formula

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Heron’s formula, once in a while known as Hero’s equation is named after Hero of Alexandria, a mathematician, and architect in 10 AD.

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photo via wikipedia

Definition for Heron’s equation

Heron’s equation gives the region of a triangle by requiring no self-assertive decision of side as base or vertex as cause, in opposition to different formulas that ascertain the territory of a triangle. The region can be determined utilizing all the three sides, particularly in scalene triangle, where none of the sides are equivalent. Most equations utilize the stature of a triangle to figure the zone.

What are the means for Heron’s equation?

As per this equation,

Region of the triangle –

A = \sqrt{s(s-a)(s-b)(s-c)},

where the semi – border of the triangle,


a, b, c are the lengths of the sides of the triangle.

Heron’s Formula Worksheet

  • Figure the semiperimeter of a triangle, s, where a = 23, b = 40, c = 35.

a. 35

b. 48

c. 25

d. 49

Right Answer-d. 49

This image has an empty alt attribute; its file name is 1920px-Triangle_with_notations_3.svg.png
photo via wikipedia
Triangle with altitude h cutting base c into d + (c − d)
  • Figure the territory of a triangle utilizing Heron’s formula, if the three sides of the triangle are, a = 5, b = 9, c = 6

a. 12.34

b. 10.6

c. 14.14

d. 13.26

Right Answer-14.14

  • Compute the side of a triangle b, if side a = 12 and side c = 6 and the semi – border rises to 13.

a. 9

b. 8

c. 6

d. 7

Right Answer-b. 8

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photo via wikipedia
Geometrical significance of s − a, s − b, and s − c. See the Law of cotangents for the reasoning behind this.

3 Interesting facts about Heron’s Formula

  • Heron’s formula has been known to mathematicians for about 2000 years.
  • Confirmation of this formula can be found in Hero of Alexandria’s book “Metrica”.
  • Numerous mathematicians accept that Archimedes definitely knew the equation before Heron. Some likewise accept that this formula has Vedic roots and the credit ought to be given to the antiquated Hindus.

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