How to Find the Area of a Triangle

A triangle is a geometrical shape that has three sides and three angles. These three angles may vary in measurement, but they always add up to 180°. If you are looking to find the area of a triangle, then let us see the formulas.

Area = (Base * Height) / 2

To find the area of a triangle, you will need to know the length of the base, and the height of the triangle. The height of the triangle is the length of a line drawn perpendicular to the base from the angle opposite the base. With these two values known, you can easily find the area using the formula.

If the height of the triangle is not known, but the length of all the sides are known, you can use Heron's formula to find the area.

Let a, b, and c be the length of the sides of the triangle.
Area = sqrt(s * (s-a) * (s-b) * (s-c))

The semi-perimeter s is given by
s = (a + b + c) / 2

The right triangle has one 90° angle. The base (b), height (h) and single right angle help define the area of a right triangle. The formula used is:

Area= ½ * base * height or ½bh

Example: Find the area of a right triangle with base 7 centimeters and height of 10 centimeters.

Solution:
A = ½*7cm*10cm
A = ½*70 cm²
A = 35 cm²

An equilateral triangle has measure of each angle as 60°. An equilateral triangle is also an isosceles triangle. The area of an equilateral triangle is calculated as:

Area = [s²3^1/2] / 4

One can find the area of a triangle on a graph by using Distance Formula and then Heron's Formula. Suppose the coordinates of the vertices were (3,5),(6,-5), and (-4,10). The distance formula is as follows:

[(3 -6)² + (5 - (-5))²] ^½ = 109^½

[(3 - (-4))² + (5 - 10)²] ^½ = 74^½

[(6 - (-4))² + (- 5 - 10)²] ^½ = 325^½

Heron's formula will help you find the area of a triangle given its three side lengths.

s = 109^½ + 74^½ + 325^½ / 2

Area = [ (s) (s- 109^½) + (s- 74^½) + (s- 325^½] ²


Area = [{(109^½) + (174^½) + (325^½)} ² / 2 ][{(109^½) + (174^½) + (325^½}² / 2 - 109^½][{(109^½) + (174^½) + (325^½}² / 2 - 74^½][{(109^½) + (174^½) + (325^½}² / 2 - 325^½]

The resultant answer will help you find the area of a triangle on a graph. These were a few examples and formulas that will help you. You should now be able to find the area of a triangle.