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
