How to prove that Area of a Triangle is equal to Half base times its height.?

Answer 1

Informal proof -- take an isosceles triangle and cut it along its altitude. You can then re-arrange it to make it into a rectangle.

Answer 2

Two congruent triangles can be arranged to form a parallelogram.
The formula for the area of a parallelogram is A=base*height.
Since the triangle is one half of the parallelogram, the area of the triangle is one half of the area of the parallelogram:
A=base*height/2

Answer 3

If you put two right triangles(a triangle that have one 90 degree angle) that have the same leg length together it equals a rectangle and by definiton of the area of a rectangle: a rectangles area is equal to the width multiplied by the length which is equal also to the area of the two triangles put together and thus if you divide this by two, you get the area of just one triangle.

good luck.