find the area of a pentagon

[Sarah&Sierra]

I need to find the area of a pentagon.[attachment=0:2ktv6y3a]3-13-2009 10;38;28 PMmath.JPG[/attachment:2ktv6y3a]

 

[Loren]

Try dividing it into two parts. At the top you have a triangle with known altitude and base. On the bottom you have a trapezoid with known bases and altitude. Can you take it from there?

 

[soroban]

Hello, Sarah&Sierra!

I need to find the area of this pentagon.

                *
              * | *
            *   |   *
          *     |6    *
        *       |       *
      * - - - - + - - - - *
       *   8    |    8   *
        *       |10     *
         *      |      *
          * * * * * * *
               10

The upper section is a triangle with base 16 and height 6.

. . \(\displaystyle \text{Its area is: }\:A \:=\:\frac{1}{2}bh \:=\:\rac{1}{2}(16)(6) \:=\:48\)


The lower section is a trapezoid with height 10 and two bases, 10 and 16.

. . \(\displaystyle \text{Its area is: }\:A \:=\:\frac{h}{2}(b_1 +b_2) \:=\:\frac{10}{2}(10+16) \:=\:130\)


Therefore, the area of the pentagon is: .\(\displaystyle 48 + 130 \:=\:178\)

 

[Sarah&Sierra]

Thank you so much. My daughter is in 5th grade. I haven't had to do this in so long. You are a life saver.