Question

somebody please help.. What is the area of the equilateral triangle? Round to the nearest square centimeter.

Answer 1

for an equilateral triangle you need to know that:
- Sides are equal a = b = c (figure 1)
- Each angle is 60 degrees (figure 1)
- Height led from the top of the base of the triangle divide into two identical special right triangles on Measures angles 30,60,90 degrees. (figure 3)

triangle with angles : 30°,60° , 90°  is the length of the sides :
1 a = a  catheus (red)
2 b = a√3  catheus (red)
3 c = 2a  hypotenuse

the product of the hypotenuse of the triangle is the value of the surface of an equilateral triangle

P = a*b = (1/2*68cm*√3)*(1/2*68cm) = (34√3cm) * (34cm) = 1156√3cm²

for notebook
You can use the model

$P = \frac{ a^{2} * \sqrt{3} }{4} = \frac{ (68cm)^{2}* \sqrt{3} }{4} = \frac{4624 \sqrt{3} cm^{2} }{4} = 1156 \sqrt{3} cm^{2}$

as soon as I add attachments - drawings