How do you prove the formula for the area of a triangle?

Answer 1

Easiest way

Draw a three inch by three inch square. add lines at one inch marks to form a small grid. draw line diagonally across to form two triangles. count the number of squares in one triangle (remember the squares with the diagonal line are only half a square)

Did you get 4 1/2?

A X B divided by two 3 X 3= 9 / 2 = 4.5

To arrive to the forumla for area of triangle, lets look at the area of square and rectanlge first: Area of square: side x side Area of rectangle: length x width Notice that the formulas for area of square and rectangle is very similar. The squre is a special case only, so there is not much difference. Let's take the special case first- area of square: Area= side x side If I want to find the area of a triangle from this square, you have to divide the square in half diagonally. This means: (side x side)/2 = area of triangle Let's take a look at retangle now: Area of rectangle: length x width Similarly like the square, you divide the rectangle diagonally by half. This means: (length x width)/2 Conclusion: Thus, area of triangle= (base x height)/2 The base can be considered as one of the sides of the rectangle/square, and the height can be considered as the other side of the rectangle/square. THE FORMULA OF TRIANGLE COMES FROM HALF THE AREA OF RECTANGLE/SQUARE! Visit quickanswerz.com for more math help and tutoring!

Area is measured in square units. If we are given a region we divide the region into unit squares.

Then we count the number squares, which is the area of the region.

Consider a rectangle of length 10 units and width 5 units.

The area of the rectangle is 50 square units.

It is because we can divide the rectangle into 10 equal parts along the length.

Similarly, we can divide the rectangle into 5 equal parts along the width. Now we have divided the entire rectangle into unit squares.

If we count the number of squares we get 50 unit squares.

We get this by multiplying the length and the width. Area = Length*Width square units.

This is the same for a parallelogram too.

Area of a parallelogram is base * height square units

This is how the concept of area has come.

We can find the area of the triangle also.

A rectangle or a parallelogram can be divided into two equal triangles by a diagonal.

Half of the area of the rectangle(or parallelogram) gives the area of the triangle.

In fact, we can extend any triangle into an parallelogram.

So, we get the formula, area of a triangle = (base* height)/2 square units.

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