From my study of trapezoids.. I've found that there is only one formula for area. That being A = 1/2(b1 + b2)h. There are several shapes for a Trapezoid and all of them allow for drawing a vertical Height, h, that forms a Right Angle from b1 to b2. Therefore, the proof above is Adequate Proof for all trapezoid Areas. Only a modification exist for a "RIGHT" Trapezium.
but if you use cavalieri's principle, you can find that the parameters for the trapezoid remain unaffected thus it's irregularity having no effect to the proof
No, it applies without a loss of generality. Its just the subdivisions are different for trapezoids with non parallel side lengths. There does exist, similiar to herron’s formula, a formula for cyclic quadrilaterals called “Bretschneiders formula”.
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Thank you, this helped a lot :)
Excellent!👍
Thanks a lot
So simple it is !
life saver
i just split it into 2 halves, 2 triangles, then use the formula which gives (bh+ah)/2 and then factor out the h on the top to give the formula
How area of a quadrilateral can be determined when its four sides are given?
Heron’s formula for quadrilaterals
There is a flaw in your proof: You only proved a trapezoid with right triangles on both of the legs. You have not proven an irregular trapazoid
From my study of trapezoids.. I've found that there is only one formula for area. That being A = 1/2(b1 + b2)h. There are several shapes for a Trapezoid and all of them allow for drawing a vertical Height, h, that forms a Right Angle from b1 to b2. Therefore, the proof above is Adequate Proof for all trapezoid Areas. Only a modification exist for a "RIGHT" Trapezium.
but if you use cavalieri's principle, you can find that the parameters for the trapezoid remain unaffected thus it's irregularity having no effect to the proof
No, it applies without a loss of generality. Its just the subdivisions are different for trapezoids with non parallel side lengths.
There does exist, similiar to herron’s formula, a formula for cyclic quadrilaterals called “Bretschneiders formula”.