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Area of a Triangle

The area of a triangle is related to the area of a rectangle. In fact, we can derive the area of a triangle from the area of a rectangle.

In the grid here, the length of the rectangle is 6 cm and the breadth is 4 cm. So its area is 24 cm2.

grid with rectangleNow assume that you are cutting this rectangle into two, along one of its diagonals (shown in dotted lines). You will get two split shapes that are right-angled triangles.

rectangle split into 2 triangles

The two triangles are identical, hence their areas are equal too. So the area of one triangle is half the area of the rectangle.

Let us look at the actual derivations of the area of a triangle for the three types of triangles –

 

Area of right-angled triangle

Area of Delta BCD is half the area of rectangle ABCD.area of right angled triangle

=  1/2 x area of rectangle ABCD

=  1/2 x (b x h)

=  {1/2}bh

 

Area of acute-angled triangle

We need to find the area of the acute-angled triangle KCD in this figure. area of acute angled triangleWe can see that this triangle KCD creates four triangles A1, A2, A3, and A4, and two rectangles AKLD and KBCL.

In the rectangle AKLD, the diagonal DK creates two right-angled triangles A1 and A2 respectively. Similarly in the rectangle KBCL, the diagonal KC creates two equal right-angled triangles A3 and A4.

So A1 = A2  and  A3 = A4

A1 + A4  =  A2 + A3

Hence area of Delta KCD =  1/2 of area of rectangle ABCD

=  {1/2}bh

 

Area of obtuse-angled triangle

We need to find the area of the obtuse-angled triangle ABD here.area of obtuse angled triangle

Area of Delta ABD = area of Delta ABC – area of Delta BCD

=  {1/2}(a~+~b)h  –  {1/2}ah

=  {1/2}ah  +  {1/2}bh  –  {1/2}ah

=  {1/2}bh

 

From these three calculations, we can see that the formula for calculating the area of a triangle is exactly the same i.e. half of base multiplied by its height.

Here are a few examples of area of a triangle.