Question

Prove that the sea of an equal triangle is equal to √3a^{2​​​​​​}\4 where a is the triangle.

Answer 1

The area of an equilateral triangle (all sides congruent) can be found using the formula
Area
=
√
3
4
s
2
where s is the length of one side of the triangle.
Try this Drag the orange dots on each vertex to reshape the triangle. The formula shown will recalculate the area using this method.

When you know all three sides of a triangle, you can find the area using Heron's Formula. But in the case of equilateral triangles, where all three sides are the same length, there is a simpler formula:

Area
=
√
3
4
s
2
where
s is the length of any side of the triangle.

Note that

√
3
4
is constant that has the value of approximately 0.433, so the formula simplifies a little to
Approximate area
=
0.433
s
s Methods for finding triangle area

If you know:	Use:
Base and altitude	"Half base times height" method
All 3 sides	Heron's Formula
Two sides and included angle	Side-angle-side method
x,y coordinates of the vertices	Area of a triangle- by formula (Coordinate Geometry) or Area of a triangle - box method (Coordinate Geometry)
The triangle is equilateral	Area of an equilateral triangle