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.
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
= x area of rectangle ABCD
= x (b x h)
Area of acute-angled triangle
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 = of area of rectangle ABCD
Area of obtuse-angled triangle
Area of = area of – area of
= + –
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.