# Thread: area of parallelograms and trapezoids

1. ## area of parallelograms and trapezoids

If NS=16 find the area of parallelogram MNOP. This problem is really hard. I need to know how to do it with work. I also know that the answer is 122 but i need work to go with it. the problem can be solved using a proof or by using algebra. Yeah sorry i forgot to mention that MN=10, RS=8, ST= 3, and OV=9. This picture is not drawn to scale.

Hello mizzell

Welcome to Math Help Forum!
Originally Posted by mizzell
If NS=16 find the area of parallelogram MNOP. This problem is really hard. I need to know how to do it with work. I also know that the answer is 122 but i need work to go with it. the problem can be solved using a proof or by using algebra.
There must be some details that you haven't told us - we don't have enough here to calculate the area. Please check the question again, and give us more information.

3. Originally Posted by mizzell
If NS=16 find the area of parallelogram MNOP. This problem is really hard. I need to know how to do it with work. I also know that the answer is 122 but i need work to go with it. the problem can be solved using a proof or by using algebra. MN=10, RS=8, ST= 3, and OV=9. This picture is not drawn to scale.
The green parallelogram is the difference of the sum of two trapezoids.
(See attachment)

2 orange - 2 blue = 1 green

4. Originally Posted by mizzell
If NS=16 find the area of parallelogram MNOP. This problem is really hard. I need to know how to do it with work. I also know that the answer is 122 but i need work to go with it. the problem can be solved using a proof or by using algebra. Yeah sorry i forgot to mention that MN=10, RS=8, ST= 3, and OV=9. This picture is not drawn to scale.
1. Compare the trapezoid RSNM with the trapezoid TVOP. You can show that VT = 8 and PT = 3.

2. Have a look here: http://www.mathhelpforum.com/math-he...rapezoids.html

5. What do u mean by compare those two trapezoids and how did u VT and PT? Also that link you gave me does not work.

6. Originally Posted by mizzell
What do u mean by compare those two trapezoids and how did u VT and PT?
Also that link you gave me does not work. <<<< it's post #3 (the mods transfered my reply to your double post into this thread)
$\displaystyle \overline{MN} \parallel \overline{PO}~\wedge~ |\overline{MN}| = |\overline{PO}|~\implies~|\overline{RS}| = |\overline{TV}|$

$\displaystyle |\overline{SN}| - |\overline{RM}| = 6~\implies~|\overline{OV}| - |\overline{PT}| = 6$

Solve for $\displaystyle |\overline{PT}|$