Home > Geometry > Perimeter and Area of Triangle

What is the area of an equilateral triangle with a side length of 1?

Answer 1

#sqrt3/4#

Imagine the equilateral being cut in half by an altitude. This way, there are two right triangles which have the angle pattern #30˚-60˚-90˚#. This means the sides are in a ratio of #1:sqrt3:2#.

If the altitude is drawn in, the base of the triangle is bisected, leaving two congruent segments with length #1/2#. The side opposite the #60˚# angle, the height of the triangle, is just #sqrt3# times the existing side of #1/2#, so its length is #sqrt3/2#.

This is all we need to know, since the area of a triangle is #A=1/2bh#.

We know the base is #1# and the height is #sqrt3/2#, so the area of the triangle is #sqrt3/4#.

Refer to this picture if you're still confused:

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Evelyn Arboleda

The area of an equilateral triangle with a side length of 1 is (√3)/4 square units, or approximately 0.433 square units.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 3

Ella Armstrong

The area of an equilateral triangle with a side length of 1 is ( \frac{\sqrt{3}}{4} ) square units.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.