The measure of the side of an equilateral triangle is 6cm. Then area of circle touching all three sides of given triangle is ------cm2 (a) pie (b) 3 pie (c) 12 pie (d) 36pie
P = 6 + 6 + 6 = 18 cm.
P/2 = 18/2 = 9 cm.
S1/2 = S2/2 = S3/2 = 6/2 = 3 cm.
At = sqrt(9*3*3*3) = 15.6 cm^2 = 5pi = Area of triangle.
Ac > 5pi = 12pi.
To find the area of the circle touching all three sides of the equilateral triangle, we can use the concept of the inradius of an equilateral triangle.
An equilateral triangle has all three sides equal in length. Since the measure of each side of the triangle is given as 6 cm, it means all three sides are 6 cm long.
The formula used to find the inradius (r) of an equilateral triangle is given by:
r = (side length √3)/6
In this case, the side length (s) is 6 cm. Therefore, substituting the value into the formula:
r = (6 √3)/6
r = √3 cm
The inradius of the equilateral triangle is √3 cm.
Now, the area of the circle touching all three sides of the triangle can be found using the formula for the area of a circle:
A = πr^2
Substituting the value of the inradius (√3 cm) into the formula:
A = π(√3)^2
A = 3π
Hence, the area of the circle touching all three sides of the equilateral triangle is 3π cm².
Therefore, the correct answer is (b) 3π.