An equilateral triangle has side lengths of 40mm, what is the area of the triangle?

Equailateral means that base=40mm

solve for height

split the triangle in half with a line perpendicular to the base

now you have 2 right triangles with base 40/2=20 and hypotonuse 40

solve for height or the other side

use pythagorean theorem

a^2+b^2=c^2

20^2+b^2=40^2

400+b^2=1600

subtract 400 fromb oth sides

b^2=1200

square root boht sides

b=√1200=20√3

the height = 20√3

area of triangle=1/2base times height

base=40

height=20√3

1/2 times 40 times 20√3=20 times 20√3=400√3

the area is 400√3 mm^2