How do you calculate the area of a triangle?

In the field of geometry we always come across different figures and one of them is the triangles. If we are to define this then the term “area” is defined as the region occupied inside the boundary of a flat object or figure. When we are to discuss about the measurement is done in square units with the standard unit being square meters (m2). If we are to do the computation of area, there are pre-defined formulas for squares, rectangles, circle, triangles, etc. we will have a look at the different parameters that are to be implemented so that we will be able to understand the computation and the sequence as well.

The area of a triangle is oftendefined as the total region that is enclosed by the three sides of any particular triangle. The area of the triangle is said to be half of the base times height, i.e. A = 1/2 × b × h. Wewill also like to learn here how to calculate the areas of the different triangles and the parameters to be used.

Example: find the area of a triangle with base b = 4 cm and height h = 6 cm?

We will use the formula,

Area of a Triangle, A = 1/2 × b × h = 1/2 × 4 cm × 6 cm = 2 cm × 6 cm = 8 cm2

We will use all the different ways that will be useful for the better application as well.

Area of a Triangle Formula

The area of the triangle is given by the formula mentioned below:

  • Area of a Triangle = A = ½ (b × h) square units

Here, b and h proves to be the base and height of the triangle, respectively.

Here we would like to understand what all are the different ways that  like an area of an equilateral triangle, an isosceles triangle, right-angled triangle,  are given below. Also, we will have a look as to how to find the area of a triangle with 3 sides using Heron’s formula with examples.

Area of a Right Angled Triangle

In the  right-angled triangle, we will see that it’s a  right triangle has one angle at 90° and the other two acute angles sums to 90°. We will see that the height of the triangle that will be the length of the perpendicular side.

  • Area of a Right Triangle = A = ½ × Base × Height(Perpendicular distance)

Area of an Equilateral Triangle

This is a triangle in which all the sides are equal. When we will draw the perpendicular from the vertex of the triangle to the base then it will divide the base into two equal parts.  The formula that is being used to calculate the area is:

  • Area of an Equilateral Triangle = A = (√3)/4 × side2

Area of an Isosceles Triangle

We will see that the isosceles triangle has got two of its sides equal where the angles opposite the equal sides are also equal.

Area of an Isosceles Triangle = A = ½ (base × height)

Perimeter of a Triangle

This is also very important that we will calculate the perimeter of the triangle. The formula for that is given below:

  • The perimeter of a triangle = P = (a + b + c) units

Where a, b and c are the sides of the triangle.

Area of Triangle with Three Sides (Heron’s Formula)

We can also find the area of a triangle with 3 sides of different measures by using Heron’s formula. This formula includes two important steps that are to be followed. The first step is to find the semi perimeter of a triangle and then by adding all the three sides of a triangle and dividing it by 2.  When we are to next step is that, then apply the semi-perimeter of triangle value in the main formula that is called “Heron’s Formula” to find the area of a triangle.

  • Area of an Isosceles Triangle = A = ½ (base × height)

 The application of the different formulas is very important so that we will be able to understand the application of the same. We will also be able to calculate the formulas that are related to different values by using different formulas.

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