Trapezoid Area Formula

Ai Ekio · #1 $Old$ 09-02-2008, 12:11 PM

Usually I can figure out problems I'm having trouble with but I just can't figure this one out.
It goes as follows:

1.Draw a trapezoid.Label it's bases and height b1, b2, and 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.

Please explain it to me.Thank you.

Soroban · #2 $Old$ 09-02-2008, 05:36 PM

Hello, Ai Ekio!

Quote:

1. Draw a trapezoid.
Label its bases and height $b_1,\:b_2,\:h$ , 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) $\Delta ABD$ has base $b_1$ and height $h.$
. . . Its area is: . $\frac{1}{2}b_1h$

. . $\Delta BCD$ has base $b_2$ and height $h.$
. . . Its area is: . $\frac{1}{2}b_2h$

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

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