Quadrilaterals • Topic 5 of 5

Trapezoids

A trapezoid is a quadrilateral with exactly one pair of parallel sides, called the bases. The other two sides are the legs. The area is the average of the two bases times the height: ½(b₁ + b₂) × h, where the height is the perpendicular distance between the bases. As with all quadrilaterals, the four angles sum to 360°. An isosceles trapezoid has equal legs and equal base angles. The most common SAT task is computing the area, so identify the two parallel sides as the bases and use the perpendicular height — not a slanted leg — in the formula. Average the bases first, then multiply by the height.

A trapezoid with parallel bases and a perpendicular heightTrapezoidb₁b₂hArea = ½(b₁ + b₂) × h

✅ Solved examples

1. A trapezoid has parallel sides 6 and 10 and height 4. Find the area.
½(6 + 10)(4) = ½ × 16 × 4 = 32.
2. Parallel sides 5 and 9, height 6. Find the area.
½(5 + 9)(6) = ½ × 14 × 6 = 42.
3. How many pairs of parallel sides does a trapezoid have?
Exactly one.
4. Parallel sides 8 and 12, height 5. Find the area.
½(8 + 12)(5) = ½ × 20 × 5 = 50.

✏️ Practice — try these, take hints as needed

1. A trapezoid has parallel sides 4 and 8 and height 5. Find the area.
½(b₁ + b₂)h.
½(12)(5).
—
30.
2. Parallel sides 7 and 11, height 4. Find the area.
½(18)(4).
—
—
36.
3. Parallel sides 10 and 14, height 6. Find the area.
½(24)(6).
—
—
72.
4. The parallel sides of a trapezoid are called the:
Top and bottom.
—
—
Bases.
5. Parallel sides 3 and 9, height 8. Find the area.
½(12)(8).
—
—
48.

📝 Topic test — 8 questions

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