Given an equilateral triangle of side 12cm , find the: A) area of the triangle
B) radius of the circumscribed circle
C) radius of inscribed circle
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Answer:
Step-by-step explanation:
s = a + b + c/2
= 12 + 12 + 12/2
= 36/2
= 18 cm
By Heron's formula,
A)Area of the triangle = √s(s-a)(s-b)(s-c)
= √18(18 -12)(18 -12)(18 -12)
= √18 x 6 x 6 x 6
= 36√3 sq. cm
B)radius of the circumscribed circle = a/√3 where a is the side of the triangle
Radius = 12/√3
=12 x√3/ √3 x √3
= 12√3/3
= 4√3 cm
C) radius of inscribed circle =√3 a/6
= √3 x 12/6
= 2√3 cm
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