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An equilateral triangle is circumscribed inside a circle with a radius of 6. What is the area of the triangle?

1 Answer

Jun 2, 2018

Area of the equilateral triangle $46.77$ $color(green)(46.77$

Explanation:

Given triangle is equilateral and the radius of the circum circle is 6.

$\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C} = 2 R$ $a / sin A = b / sin B = c / sin C = 2R$ where R is the radius of the circum circle.

$ˆ A = ˆ B = ˆ C = \frac{π}{3}, a = b = c$ $hat A = hat B = hat C = pi/3, a = b = c$ being an equilateral triangle.

$:. a = b = c = 2R sin A = 2 * 6 * sin (pi/3) = 6sqrt3$

Area of triangle $A_t = (sqrt3/4) a^2$

$A_t = (sqrt3/4) (6sqrt3)^2 = 27sqrt3 = color(green)(46.77$

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