Expert: Paul Klarreich - 9/28/2008

Question
hi paul..
i need your help on this trapzium question..it says:
a trapezium has paraell sides of a and b with a perpendicular height h. the trapezium is rotated by 180 degrees and two trapezia are put together. prove that the area of a trapezium is 1/2 h(a+b)

Answer
Questioner:   umayr
Category:  Advanced Math
Private:  No
 
Subject:  area of a trapezium
Question:  hi paul..
i need your help on this trapzium question..it says:
a trapezium has paralell sides of a and b with a perpendicular height h. the trapezium is rotated by 180 degrees and two trapezia are put together. prove that the area of a trapezium is 1/2 h(a+b)
-------------------------------------------------
Hi, Umayr,

[I think they are called 'trapezoids' here.]

This is a pretty standard proof and there are others.  All you need is this picture:
    p a        b        Q
    -------------------- +
   /     \             / |
  /       \           /  |
 /         \         /   |
/           \       /    |
/             \     /     |
-------------------- . . .+
S      b         a R

and the observations that:

1. PQRS is a parallelogram.
2. PQRS contains two copies of the trapezoid.
3. The area of a parallelogram is  base * height = h(a + b)

That should do it.