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

629 cm2

363 cm2

982 cm2

1257 cm2

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. 

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