What is the area of an equilateral triangle inscribed in a circle of radius $4\ cm$?
- $12{ cm }^{ 2 }$
- $9\sqrt { 3 } { cm }^{ 2 }$
- $8\sqrt { 3 } { cm }^{ 2 }$
- $12\sqrt { 3 } { cm }^{ 2 }$
Reveal answer
Fill a bubble to check yourself
D
Correct answer
Explanation
For an equilateral triangle inscribed in a circle of radius R, the side length s = R * sqrt(3). With R = 4, s = 4 * sqrt(3). The area is (sqrt(3)/4) * s^2 = (sqrt(3)/4) * (16 * 3) = 12 * sqrt(3).
AI explanation
The formula for the area of an equilateral triangle inscribed in a circle of radius R is (3 times the square root of 3 times R squared) divided by 4. Substituting the given radius of 4 cm into the formula gives (3 times the square root of 3 times 4 squared) divided by 4. Simplifying the expression gives 3 times the square root of 3 times 16 divided by 4, which equals 12 times the square root of 3 square cm. The result is 12 times the square root of 3 square cm.