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Trapezoid Area

A=a+b2⋅hA = \frac{a + b}{2} \cdot h

Worked example: sides 3 m and 5 m, height 4 m → 16 m^2 — press Try an example to run it live, then adjust anything.

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Grade 10Grade 10 Math

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Trapezoid Area explained

abhA

A trapezoid's area is the average of its two parallel sides multiplied by the perpendicular distance between them. The proof fits in one picture: take a second, identical trapezoid, flip it upside down, and snug it against the first — together they form a parallelogram with base (a + b) and height h, so one trapezoid is half of that. Area rules of exactly this kind appear in the Rhind papyrus, where Egyptian scribes around 1550 BC computed the areas of tapering fields along the Nile.

The formula still earns its keep in civil engineering: a drainage channel with a 3 m bottom, a 5 m top, and a 1.2 m depth has a cross-section of (3 + 5)/2 × 1.2 = 4.8 m², the number that sets how much water it can carry. As always, h must be measured perpendicular to the parallel sides — never along a slanted leg.

Trapezoid Area formula

A=a+b2⋅hA = \frac{a + b}{2} \cdot h
Where
  • AA= Area (m²)
  • aa= Parallel side a (m)
  • bb= Parallel side b (m)
  • hh= Height (m)

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