Area of a Trapezoid

1. 1Two Bases, One HeightUnlike a triangle, a trapezoid has two different bases. That is what makes its area formula less obvious.(8 + 4) × 5 = 60?
2. 2A Copy Is BornA copy identical to the trapezoid peels off the original itself — same bases, same height, same slanted sides — and parks beside it.Two identical trapezoids
3. 3Pair Them UpRotate the twin half a turn and join it along the slanted side. The two trapezoids lock into a parallelogram whose base is 8 + 4 = 12 cm and whose height is still 5 cm.Base 12 cm · Height 5 cm
4. 4Measure the ParallelogramAlong the long edge, the twin's top base continues the original's bottom base: 8 + 4 = 12 cm. The dashed rectangle has the same base and the same height, so it has the same area: 12 × 5 = 60 cm².12 × 5 = 60 cm²
5. 5Halve ItThe parallelogram holds exactly two trapezoids, so one trapezoid is half of it: ((8 + 4) × 5) ÷ 2 = 30 cm². The ÷ 2 grows out of the seam itself.S = ((a + b) × h) ÷ 2
6. 6Check on the FigureCheck backwards on the figure itself: 30 × 2 = 60. Double the answer and the twin lights back up — the pair rebuilds the parallelogram we measured.30 × 2 = 60 ✓
7. 7The Whole TrickA trapezoid is half of its doubled parallelogram: add the two bases, multiply by the height, then halve. The area is 30 cm².S = ((8 + 4) × 5) ÷ 2 = 30 cm²

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