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The triangle is a polygon with the least number of sides. This fact that the triangle encloses a well defined plane region made it possible to find the perimeter enclosing and the area enclosed using formulas.

Measurement problems on plane figures mainly involve perimeter and area. The two formulas for a general scalene triangle are

**Perimeter of a triangle = a + b + c**

where a, b and c are the lengths of the sides of the triangle.

**Area of a triangle = $\frac{1}{2}$.bh**

Where 'b' the base is the length of a side and 'h' the corresponding height.

Measurement problems on plane figures mainly involve perimeter and area. The two formulas for a general scalene triangle are

where a, b and c are the lengths of the sides of the triangle.

Where 'b' the base is the length of a side and 'h' the corresponding height.

2s = a + b + c

Area = $\sqrt{}$s(s - a)(s - b)(s - c)

Area of an equilateral triangle of side ‘a’ = $\frac{\sqrt{3a^2}}{4}$

An equilateral triangle is a triangle with three congruent sides. This attribute simplifies the formulas for perimeter and area further.

Since the three sides are of equal lengths in an equilateral triangle, a = b = c.

**Perimeter of equilateral triangle = 3a**

Where a is the length of the side.

Since the three sides are of equal lengths in an equilateral triangle, a = b = c.

Where a is the length of the side.

The equiangular property of an equilateral triangle enables the h to be written in terms of the base.

In the equilateral triangle each side is of length a units, and each angle measures 60o. CD is the altitude drawn to side AB Applying Pythagorean theorem for the right triangle ADC, h ^{2}+$(\frac{a}{2})^2$=a^{2}→h^{2}+$\frac{a^2}{4}$=a^{2}h ^{2}+$\frac{3a^2}{4}$→h = $\frac{\sqrt{3}}{2}$ |
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Height of an equilateral triangle of side 'a' = $\frac{\sqrt{3a}}{2}$ |