A triangle that has all sides of the equal length is called an equilateral triangle. It is also equiangular with internal angles 60° each in measurement. It’s all sides are congruent to one another.

Different Equilateral Triangle Formulas can be its perimeter, area

Perimeter= 3a , where a is the length of the side

Area= 34a2 sq. units

Height= altitude from any side of an Equilateral Triangle,

h= 32a units

Volume= ( 34)a2h [ equilateral triangular prism]

### Solved Examples

Q1. Find the perimeter of an equilateral triangle with side 5cm.

Ans. Perimeter= 3a= 3×5= 15cm

Q2. Find the area of an equilateral triangle with side 10cm. Determine its height.

Ans. Area=34a2 = 34(10)2= 253 square units.

h= 32(10)= 53 square units.

Q3. Find the area of an equilateral triangle when the height given is 33.

Ans. Height, h= 32a units

33 = 32 a

a= 33 x 23

a= 6

∴ Side= 6cm

Area= 34a2 = 34(6)2 = 34 x 36 = 93 square units.

Area can also be found using the formula: ½ x base x height= ½ x 6 x 33

= 93 square units.

∴ Area= 93 square units.