Question

Why do we use the formula a+b divided by 2 to find the area of a trapezoid

Answer 1

Answer:

So for our trapezium, the top side length is a, the bottom side length is b and the height is h.

So assuming b > a, b - a will give the length of the base of the two triangles. So you now have a rectangle, a by h (and the area ah)  and two triangle, each with a base of (b-a)/2 triangle and height h. The area of the two triangles is just (b-a)/2 * h or h(b-a)/2.

The total area is h(b-a)/2 + ah = h(b-a)/2 + 2ah/2 = h(b-a+2a)/2 = h(b+a)/2

Step-by-step explanation:

Look at the picture