Question

Find the area of an equilateral triangle with radius 22 cm. Round to the nearest whole number.

Answer 1

In this item, we are given with the radius equal to 22 cm.

This measurement of the radius is the hypotenuse of the 30°-60°-90° triangle formed with the half the measurement of the side of the equilateral triangle being opposite to the 60°  and equal to the hypotenuse times (1/2)(√3)

If we let s be the side of the triangle then,
                 s/2 = r(1/2)(√3)
Multiplying the equation by 2,
                 s = r√3
Substituting,
              s = (22 cm)(√3) = 22√3

The area of the equilateral triangle is computed through the equation,
         A = (√3 / 4)(s²)
Substituting,
         A = (√3 / 4)(22√3)² = 628.7 cm²

Therefore, the answer to this item is the first choice.