Question

find the area of a circle circumscribing an equilateral triangle of side 15 cm

Answer 1

Sol:

Height of an equilateral triangle (h) = √3 /2 (l) where l is the side of the equilateral triangle.

h = √3 /2 (15)

In an equilateral triangle the orthocenter, centroid, circumcenter and incenter coincide.

The center of the circle is the centroid and height coincides with the median. The radius of the circumcircle is equal to two thirds the height.

Formula for the Radius of the Circumcircle = 2/3 h

= 2/3 x √3 /2 (15)

= 5 √3 cm

Area of the circle = πr2

= 22/7 x 5 √3 x 5 √3

= 1650 / 7 cm2

Answer 2

Height of an equilateral triangle (h) = √3 /2 (l) where l is the side of the equilateral triangle. h = √3 /2 (15)

In an equilateral triangle the orthocenter, centroid, circumcenter and incenter coincide.

The center of the circle is the centroid and height coincides with the median. The radius of the circumcircle is equal to two thirds the height.

Formula for the Radius of the Circumcircle = 2/3 h = 2/3 x √3 /2 (15) = 5 √3 cm Area of the circle = πr2

= 22/7 x 5 √3 x 5 √3 = 1650 / 7 cm2