Hello, Ai Ekio!

1. Draw a trapezoid.

Label its bases and height $\displaystyle b_1,\:b_2,\:h$, respectively.

Then draw a diagonal of the trapezoid.

(a) Write an expression for the area of each of the two triangles.

(b) Explain how you can justify the trapezoid area formula

using the areas of the two triangles. Code:

b2
B * * * * * * C
*: * *
* : * *
* :h * *
* : * *
* : * *
A * * * * * * * * * D
b1

(a) $\displaystyle \Delta ABD$ has base $\displaystyle b_1$ and height $\displaystyle h.$

. . . Its area is: .$\displaystyle \frac{1}{2}b_1h$

. . $\displaystyle \Delta BCD$ has base $\displaystyle b_2$ and height $\displaystyle h.$

. . . Its area is: .$\displaystyle \frac{1}{2}b_2h$

(b) The area of the trapezoid is the sum of the areas of the two triangles.

. . $\displaystyle A \;=\;\frac{1}{2}b_1h + \frac{1}{2}b_2h \quad\Rightarrow\quad A \;=\;\frac{1}{2}h(b_1+b_2)$