Find the area of an equilateral triangle with apothem 7 cm. Round to the nearest whole number

In equilateral triangle all sides are equal = x,

from right triangle that is formed by apothem, height 7*3 = 21

hypotenuse / opposite leg = sin angle,

hypotenuse is a side of triangle = x, opposite leg is apotheme = 21,

angle in equilateral triangle = 60⁰

21/x = sin 60, x*sin60=21, x=21/sin60, x=21 / (√3/2), x=42/√3

Area of triangle = 1/2 x*x*sin angle

Area of triangle = 1/2 * 42/√3*42/√3*sin 60=1/2 * (42²/3) * (√3/2) ≈ 255 cm²

this is just second way to do this problem, that I did at first (either way is correct)

apothem divides one side by half,

so we get small right triangle with sides x hypotenuse, x/2 is one leg, and 21 is another leg

by Pythagorean theorem

x² = (x/2) ² + 21²

x²-x²/4=441

3x²/4=441

3x²=441*4=1764

x²=1764/3

x=42/√3

Area of triangle = 1/2*base * height = 1/2*42/√3 * 21≈255 cm²