area of triangle - What is the area of the circumscribed circle of an equilateral triangle of side a = 5 inches?

Krishna (last edited 2 months ago) (Expert, Educator @Qalaxia)

Step 1; Find the relationship between the (a)side of the equilateral and (r)radius of the circumscribed circle.

NOTE: Radius of the circumscribed circle R = a * \frac{\sqrt{3}}{3}

Step 2: Find the radius of the circumscribed circle

R = 5 * \frac{\sqrt{3}}{3}

Step 3: Recall the area of the circle formula and substitute the radius value in the formula.

NOTE: Area of the circle \pi r^2

= \pi (5 * \frac{\sqrt{3}}{3})^2

= 3.14 * 25 * \frac{3}{9}

= 3.14 \frac{25}{3}