How to Find the Area of a Triangle

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°. There are three types of triangles that help you know how many sides or angles are equal. Let us see which are these three triangles.

Types of Triangles

In a triangle all three sides and angles may be equal or only two sides and angles may be equal. In the third type there are no sides or angles that are equal in measurement. These three triangles have specific names, as follows:

• Equilateral Triangle: The equilateral triangle has all three sides equal in length. The three equal angles always measure 60°.
• Isosceles Triangle: The isosceles triangle has two sides equal and two equal angles.
• Scalene Triangle: The scalene triangle has no equal sides or angles.

Types of Angles

Not only are the triangles known by the number of equal sides and angles, but even by the type of angle. The triangles have angles and each angle is also known by a different name. The following are the types of angles in a triangle:

• Acute Angle Triangle: This triangle has all the three angles less than 90°.
• Right Angle Triangle: The right angle triangle has one angle that measures exactly 90°
• Obtuse Angle Triangle: The obtuse triangle has one angle that measures more than 90°.

Area of a Triangle

The function of the base and height gives us the area of the triangle; you need to multiply the base by the height and divide by 2.

The height of the triangle is the length of the line drawn perpendicular to the base from the angle that is opposite to the base. The formula to calculate the area of a triangle is:

A = (Base x Height) / 2

Area of a Triangle if Length of All Three Sides are Known

When the length of all three sides (a, b, c) are known, you can find the area of the triangle by Heron's formula also known as Hero's formula. The Heron's formula is as follows

Let a, b, c be the length of the sides of the triangle. Then semi perimeter s is given by

s = (a + b + c) / 2

Area of the triangle is given by,

A = sqrt(s × (s-a) × (s-b) × (s-c))

How to Find the Area of a Right Triangle?

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

½ x base x height or ½bh.

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

Solution:

A = ½ b.h
A = ½ . (7cm). (10cm)
A = ½ . (70 cm²)
A = 35 cm²

How to Find the Area of an Equilateral Triangle?

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

Area of a Triangle on a Graph

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

The Heron's formula is as follows that 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. I hope you find this article useful and are now able to determine the area of a triangle.