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How to find area of triangle using Heron's formula?

Please!!! :) anyone..

Sagot :

Joecelidn

First, find it's perimeter then divide it by 2. 
s = (a + b + c) ÷ 2

Then to find the area:
A = √s(s-a)(s-b)(s-c)

That's Heron's formula for area of triangle ☺
Heron's Formula for area of triangle given sides a, b, and c; and NOT base and height:

Area = [tex] \sqrt{s(s-a)(s-b)(s-c)} [/tex]

Where s is the semi-perimeter (half of the perimeter) of the triangle.

s = [tex] \frac{1}{2} [/tex] (a + b + c)

How to use Heron's formula?
Given the sides a, b, and c of a triangle, solve its semi-perimeter first, then find the area.

Example:
The triangle has sides 3 cm, 4 cm and 5  cm.

Semi-perimeter:
s = [tex] \frac{1}{2} [/tex](3 + 4 + 5)
s = ¹/₂ (12)
s = 6

Solve for area given s (6 cm) and sides a=2 cm; b=4cm;  c=5 cm

Area =  [tex] \sqrt{(6cm)(6cm-3 cm)(6cm-4cm)(6cm-5cm)} [/tex]

Area = [tex] \sqrt{(6cm)(3cm)(2cm)(1cm)} [/tex]

Area = [tex] \sqrt{36cm ^{4} } [/tex]

Area = 6 cm²

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In finding the radius of the circumscribing circle of a triangle, the formula in solving for radius is derived from Heron's formula.  You may check the problem I solved her in brainly at link:  brainly.ph/question/275941
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