Question

The formula for the area of a trapezoid is A = 1/2 (b+b) h. Explain why the bases of a trapezoid need to be added in the formula

Answer 1

Step-by-step explanation:

Look at the picture.

We connect two congruent trapezoids as in the picture.

We created a parallelogram with a base length of b₁ + b₂ and a height h equal to the height of the trapezoid.

The formula of an area of a parallelogram:

$A_p=(base)(height)\to A_p=(b_1+b_2)h$

The area of the trapezoid is half of the parallelogram area.

Therefore we have the formula of an area of trapezoid:

$A_t=\dfrac{(b_1+b_2)h}{2}$

Therefore we need to be added the bases of a trapezoid.