# Thread: Area of Triangles in Trapezoid

1. ## Area of Triangles in Trapezoid

How do you prove the area of Triangle A is congruent to Triangle B in this trapezoid?

2. ## Re: Area of Triangles in Trapezoid

How do you prove the area of Triangle A is congruent to Triangle B in this trapezoid?
Do you have the lengths of the sides of the trapezium?

3. ## Re: Area of Triangles in Trapezoid

No i don't have lengths. It is supposed to apply to any trapezoid. Now i found this link Trapezoid -- from Wolfram MathWorld which gives formulas as to why the areas are equal. But i don't understand why.

4. ## Re: Area of Triangles in Trapezoid

No i don't have lengths. It is supposed to apply to any trapezoid. Now i found this link Trapezoid -- from Wolfram MathWorld which gives formulas as to why the areas are equal. But i don't understand why.
Only having the area of the two triangles equal, does not imply that they are congruent.

5. ## Re: Area of Triangles in Trapezoid

You are right badhi. So i guess the question is why do they have the same area?

6. ## Re: Area of Triangles in Trapezoid

How do you prove the area of Triangle A is equal to Triangle B in this trapezoid?
Code:
            P       Q
-         *-------*
:        *   *  *   *
:       *  A  * *  B  *
:      *    *      *    *
h     *   *           *   *
:    *  *       C        *  *
:   * *                     * *
:  **                          **
- *-------------------------------*
S                               R

$\Delta PSR\text{ and }\Delta QSR\text{ have the same base (SR) and the same height (h).}$

$\text{Hence: }\:\text{area}(\Delta PSR) \;=\;\text{area}(\Delta QSR)$
. . . . . . . . . . $A + C \;=\;B + C$

$\text{Therefore: }\qquad\quad\; A \;=\;B$

7. ## Re: Area of Triangles in Trapezoid

Wow Soroban its that simple? I was trying to prove it by somehow by showing Triangle C was congruent to the Triangle with base PQ ( i guess we can call it D). which it is. Could i have used this information to prove A=B?