Area and Perimeter • Topic 4 of 6

Trapezoids

A trapezoid has one pair of parallel sides (the bases), and its area is the average of those bases times the perpendicular height: ½(b₁ + b₂) × h. Add the two parallel sides, halve the sum, then multiply by the height between them. For bases 6 and 10 with height 4, the area is ½(16)(4) = 32. Use the perpendicular height, not a slanted leg, and be sure you are averaging the two parallel sides — not the legs. The SAT mostly asks for the area directly, so the work is identifying the two bases and the height correctly and then applying the formula.

A trapezoid with parallel sides 6 and 10 and height 4Trapezoid area6104Area = ½(6+10)×4 = 32

✅ Solved examples

1. A trapezoid has bases 6 and 10 and height 4. Find its area.
½(6 + 10)(4) = ½ × 16 × 4 = 32.
2. Bases 5 and 9, height 6. Find the area.
½(14)(6) = 42.
3. Bases 8 and 12, height 5. Find the area.
½(20)(5) = 50.
4. Bases 3 and 7, height 10. Find the area.
½(10)(10) = 50.

✏️ Practice — try these, take hints as needed

1. A trapezoid has bases 4 and 8 and height 5. Find its area.
½(b₁ + b₂)h.
½(12)(5).
—
30.
2. Bases 7 and 11, height 4. Find the area.
½(18)(4).
—
—
36.
3. Bases 10 and 14, height 6. Find the area.
½(24)(6).
—
—
72.
4. Bases 2 and 8, height 9. Find the area.
½(10)(9).
—
—
45.
5. Bases 6 and 6, height 5. Find the area.
½(12)(5).
—
—
30.

📝 Topic test — 8 questions

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