# Area of Triangles in Trapezoid

• Jun 16th 2011, 08:25 PM
Area of Triangles in Trapezoid
How do you prove the area of Triangle A is congruent to Triangle B in this trapezoidAttachment 21679?
• Jun 16th 2011, 08:27 PM
Prove It
Re: Area of Triangles in Trapezoid
Quote:

How do you prove the area of Triangle A is congruent to Triangle B in this trapezoidAttachment 21679?

Do you have the lengths of the sides of the trapezium?
• Jun 16th 2011, 08:30 PM
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.
• Jun 16th 2011, 10:11 PM
Re: Area of Triangles in Trapezoid
Quote:

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.
• Jun 17th 2011, 04:32 AM
Re: Area of Triangles in Trapezoid
You are right badhi. So i guess the question is why do they have the same area?
• Jun 17th 2011, 05:01 AM
Soroban
Re: Area of Triangles in Trapezoid

Quote:

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

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

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

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

• Jun 17th 2011, 05:18 AM