Trapezoid Area — Double It into a Parallelogram
Why is a trapezoid ½(a+b)·h? Flip a copy onto it and you get a parallelogram — so one trapezoid is half.
Do not write an equation yet. Shake the figure first.
Play the reversal slowly
Now move the same pieces step by step and prove that the pattern you touched was not an accident.
A trapezoid with parallel sides a, b and height h. Its area?
Return to the exact question
Show that a trapezoid with parallel sides a, b and height h has area ½(a+b)·h, by dissection.
Why this approach works
Make a pair. Copy the trapezoid, rotate it 180°, and fit it against the slanted side: top and bottom swap to form one straight line, so the two trapezoids become a single parallelogram of base a+b and height h. Its area is (a+b)·h, so one trapezoid is half — ½(a+b)·h.
Proof
A 180°-rotated copy joins to form a parallelogram of base a+b and height h. Two trapezoids make one parallelogram, so each is ½(a+b)·h.
Try it yourself
Shrink the top side a to 0: the trapezoid becomes a triangle and ½(0+b)h = ½bh — the triangle formula.
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