Area of the triangle is calculated by the formula ½ x base x height. We will be discussing this formula in an experimental way by converting it into a rectangle. You can yourself derive the formula instead of just memorizing it and understand the real meaning of it.
Hello Friends,
Today we are going to find out area of the simplest polygon, the Triangle. We know that area of the triangle is given by the formula ½ x base x height. How can we find out this formula?
Materials required: cutout of a rectangle, marker, scale and scissors
Procedure:
Mark the length and breadth on the rectangle.
Mark any point on the top of the rectangle. From this point draw a straight line towards one corner of the rectangle.
Then draw another straight line towards the opposite corner of the rectangle.
We get a triangle whose base is same as the length of the rectangle and height is same as the breadth of the rectangle.
Cut the straight lines drawn (two sides of the triangle) to get three separate triangular cutouts.
Arrange the smaller two triangles over the bigger triangle, you will observe that the two smaller triangles fit exactly over the bigger triangle.
Thus the combined area of the two triangles is same as the bigger triangle. Which mean you could make two equal sized triangles from a rectangle.
Hence we have found that area of the triangle is half the area of the rectangle.
We have,
Area of the rectangle = 2 x Area of the triangle
length x breadth = 2 x Area of the triangle
½ l x b = Area of the triangle
= ½ height x base (length of rectangle = height of the triangle)
Area of the triangle = ½ height x base
Thus, you have derived the formula and now you know the reason Why area of the triangle is ½ height x base?
Thanks!
Team: Ashok Rupner, Chaitanya Mungi, Shanti Pise, Neha Apte
Music: Dr. Manasi Kulkarni