In <span>equilateral triangle all sides are equal =x, from right triangle that is formed by </span>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) <span> 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 </span>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
