Question

How is the formula for the area of a trapezoid derived from the formula for the area of a triangle?

Answer 1

`A = 1/2(b_1 + b_2)h`

If we cut a trapezoid by its diagonal into two triangles, we get two triangles. Both triangles have the same height `h`, which is also the height of the trapezoid. The upper base `b_1` of the trapezoid is also the base of the triangle on top. Meanwhile, the lower base `b_2` of the trapezoid is also the base of the lower triangle

The formula for the area of a triangle is

`A_t = 1/2bh`

`=> A_t = 1/2b_1h`

`=> A_l = 1/2b_2h`

If we combine the area of the two triangles, we get the area of the trapezoid.

`A = A_t + A_l`

`=> A = 1/2b_1h + 1/2b_2h`

`=> A = 1/2h(b_1 + b_2)`

`=> A = 1/2(b_1 + b_2)h`