Area of a Triangle

WHAT IS THE AREA OF A TRIANGLE?

Also known as tri-side polygon, the area of a triangle is referred to as the total enclosed by its three sides. Triangle is a 2-dimensional figure with three sides and three vertices; hence the area between the three sides is defined as its area. The base formula for the area of a triangle is:

A=1/2 × (b × h) m2

This formula applies to each triangle form, ranging from an isosceles triangle to an equilateral triangle. One thing to keep in mind here is the base, and the height of the triangle is always perpendicular to each other. The measurement of the area is done in square units, with the standard unit remaining to be square meters (m2).

AREA OF DIFFERENT TYPES OF TRIANGLES

RIGHT-ANGLED TRIANGLE 

The right-angled triangle, as the name suggests, is a right triangle that has an angle of 90°, and the angles on the other two sides are acute angles summing to 90°. In the case of a right-angled triangle, the triangle’s height will always be on the perpendicular side. Therefore, the area of the right-angled triangle is:

A= ½ × Base × Height (Perpendicular distance)

EQUILATERAL TRIANGLE 

In an equilateral triangle, all the sides of the triangle are equal. When a perpendicular is drawn from the vertex of the triangle to the base, it divides the triangle into two halves. To calculate the appropriate area of the equilateral triangle, we must know the correct measurement of the sides. The area of an equilateral triangle is calculated by:

A= (√3)/4 × side2

ISOSCELES TRIANGLE 

An isosceles triangle has the unique feature of having two equal sides, and the angles formed on these equal sides are also equal. The area of an isosceles triangle is calculated by:

A= 1/2 b√(a2 – b2 /4)

TRIANGULAR PRISM 

A triangular prism is formed with three rectangular faces and two parallel triangular bases. The surface area of the triangular prism is the sum of its exterior surfaces.

 The area of a triangular prism is calculated as follows:

A=ab+3bh

Ab is the area of the two bases and 3bh signifies the 3 rectangular sides.

Here a,b are the sides of the base and h is the height of the prism.

AREA OF TRIANGLE USING HERON’S FORMULA 

Sometimes you may find a triangle with all its sides with different measurements. The area of such a triangle could be found easily with the heron’s formula. The steps to find an area with the heron’s formula is as follows:

Calculate the semi-perimeter of the triangle by adding all three sides and dividing it by 2. The formula is s = (a+b+c) / 2

In the next step, the value of the semi-perimeter into the heron’s formula to calculate the area. A=√s(s-a)(s-b)(s-c)

AREA OF TRIANGLE GIVEN TWO SIDES AND ONE ANGLE (SAS)

Now, sometimes there may be a situation where measurements of two sides are given, and one angle is given. In such cases, what should be the steps to be taken to calculate the area of the triangle. 

Let us assume that a triangle ABC exists, with its vertex angles as ∠A, ∠B, and ∠C and sides a, b, c, respectively. 

If the sides and the angle between them are given, the following formulas can be used to find the area. 

 Area (∆ABC) = ½ bc sin A

 Area (∆ABC) = ½ ab sin C

 Area (∆ABC) = ½ ca sin B

 AREA OF TRIANGLE USING COORDINATE GEOMETRY 

 Since the area of a triangle is the space, it covers within its 3-sides and 3-vertices on 

 a Plane two-dimensional surface. Firstly, we need to find the length of the its 3-sides of 

 the triangle. The formula we need to follow to find the area on the coordinate

 the plane is as follows:

 Let us assume a triangle PBC, whose coordinates P, B, and C are given as (x1, y1), 

 (x2, y2), (x3, y3) respectively.

 Area of triangle PBC= ½ [x1( y2-y3) + x2(y3-y1) + x3(y1-y2)]