What is the area of an equilateral triangle who sides are 10?

Question

How do I set this up? I know that an equilateral triangle is two 30-60-90 triangles but how do I divide the 10s into each triangle?

Answer 1

draw an equilateral triangle

draw the height from the top vertex to the bottom horizontal side

this line segment divides the triangle into two congruent right triangles

this line segment also divides the bottom horizontal side into two congruent line segments, each 5 units in length

the height is the longer leg of the right triangles

taking one right triangle...

the hypotenuse is 10 and the shorter leg is 5

using the Pythagorean Theorem

10²=h²+5²

100=h²+25

100-25=h²

75=h²

h=√75=√25*3=5√3

A=(1/2)(10)(5√3)

A=(5)(5√3)

A=25√3

A=25*1.732

A=43.3 square units

Answer 2

Sam,

an equilateral triangle is not two 30-60-90

an equilateral triangle is 60-60-60

 

Area, a = ½*10*10*sin(60°)= 43.3unit²

 

I hope this helps you