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Please refer to image. Is there a simpler way to visually prove the scalene trapezoid area formula?

Scalene trapezoid area proof

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    $\begingroup$ The way I was taught at school was by prolonging each base by a segment of the same length as the other one (in the same half plane with respect to some side), and then remark that the resulting figure was a parallelogram with base $(a+b)$, height $h$ and double the area. $\endgroup$ – Saucy O'Path Jan 20 at 17:47
  • $\begingroup$ Thanks Saucy. Looks like Hagen von Eitzen has visualised this for us. $\endgroup$ – Dave Kirkby Jan 21 at 16:59
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Add a rotated copy of your trapezoid to form a parallelogram of twice the area.

enter image description here


In case you forgot that this parallelogram has area $(a+b)h$, note that the triangles in the following image are congruent, hence the area of the parallelogram equals that of the rectangle.

enter image description here

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  • $\begingroup$ Thanks Hagen. That is a lot simpler. $\endgroup$ – Dave Kirkby Jan 21 at 17:00

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