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Area of a Triangle


Triangles

In this blog you will come across different concepts related to triangles, it's area and how to calculate it. Different types of triangles will be discussed along with it's area calculation. We will start with the Area and then will shift to the measurement of triangles.


What is Area?

The inner surface of any shape can be known as the area of that shape or the surface in between the boundary walls is known as the area. Area is calculated in different was depending on the shape of the surface. We can also define the area as the space occupied by the 2-D surface. Different shapes have different formulas according to which we can calculate the area.


What is Triangle?

As the name suggest "Tri" "angles" this mean that any object or shape which is 2-D and having three angles are known as triangle. This is one of the important shape in geometry and trigonometry. There are three types of triangles in total known as Equilateral, Isosceles and scalene. The triangles can also be differentiated based on the angles like right, acute and obtuse. Right angle triangle is the most known; Pythagoras theorem is also based on the Right Angle Triangle.


Area of a Triangle.

The space enclosed by the three sides of the of any triangle is known as the area of a triangle. Mathematically, area of a triangle can be represented by (1/2)bh. Here "b" represent the base while "h" represent the height of the triangle. As we know that a rectangle is composed of two triangles if cut diagonally. Therefore, the formula of triangle is generated from the formula of rectangle which is b X h. It is explained deeply in the figure below:

Right angle Triangle

The above diagram explains everything deeply. In addition, the area of a triangle is measured in meter square (m2) or centimeter square (cm2).

Example:

Suppose a triangle has height 6cm and base 4cm. calculate the area?

Solution:

Area of triangle = (1/2) (bxh)

= (1/2) (24cm2)

= 12 cm2 (ANS)


Equilateral triangle and it's Area.

As the name can be divided into two parts one is "equi" which mean equal while lateral means sides. So that triangle which have equal sides are known as equilateral triangle. The formula to calculate the area of equilateral triangle is (3/4) (a2). Here a is the length of the side of the triangle. In calculation of the area of equilateral triangle we need the length of only one side.


Example:

Find the area of equilateral triangle having the side 6cm in length.

Solution:

Area = (3/4) (a2)

Area = (3/4) ((6)2)

Area = (3/4) (36)

Area = 15.588 cm2

Right angle Triangle and it's Area.

In right angle triangle the two sides have exactly an angle of 90 degree. These two sides known as height and base are perpendicular to each other while the third side is exactly opposite of them known as hypotenuse. Hypotenuse is the square of the two side height and base, this is the longest side in length. Area of right angle triangle can be calculated by the formula (1/2) (bh). If height of the triangle is not known so we can find it by Pythagoras theorem.


Example:

Find the area of a right angle triangle having base 16 cm and other sides 14 cm.

Solution:

As base is known and height is not. Therefore, we will use Pythagoras theorem to identify the height of the triangle, which is the requirement of area formula.

first of all, divide the base into two parts which is the requirement of Pythagoras theorem.

Base = 16/2 = 8cm.

a2 + b2 = c2

a2 + (8)2 = (14)2

a2 = 196 - 64

a2 = 132

Applying square root on b/s

a = 11.48 cm.

Now we have height and base, therefore putting values in the Area of right angle triangle formula:

Area = 1/2 (bh)

Area = 1/2 (08 x 11.48)

Area = 45.95 cm2


An isosceles triangle and it's Area.

A triangle which have two equal sides is known as an Isosceles triangle. The formula for area calculation is same as that of right angle triangle. The height will also be calculated in the same way. But here the base will not be divided by two and it will remain same.


Example:

If the base is 16 cm and other sides are 14 cm, height is 11.48. Find Area of an Isosceles triangle.

Solution:

Area = 1/2 (bxh)

Area = 1/2 (16 x 11.48)

Area = 1/2 (183.68)

Area = 91.84 cm2


These were some of the known triangles and how we can find their Area. Hopefully, this Article will help you understand the basic concepts related to triangles and it's area.

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