Area and Perimeter • Topic 3 of 6

Triangles

A triangle’s area is ½ × base × height, where the height is the perpendicular distance from the base to the opposite vertex — not a slanted side. Any side can be the base, as long as you pair it with the matching perpendicular height. For a base of 10 and height 6, the area is ½ × 10 × 6 = 30. The most common mistake is forgetting the ½, which halves the answer, or using a slanted side instead of the true height. The SAT supplies the base and the perpendicular height directly in most cases; multiply them and take half.

A triangle with base 10 and height 6Triangle area106Area = ½ × 10 × 6 = 30

✅ Solved examples

1. A triangle has base 10 and height 6. Find its area.
½ × 10 × 6 = 30.
2. A triangle has base 8 and height 5. Find its area.
½ × 8 × 5 = 20.
3. A triangle has base 12 and height 7. Find its area.
½ × 12 × 7 = 42.
4. A triangle has area 24 and base 8. Find its height.
24 = ½ × 8 × h, so h = 6.

✏️ Practice — try these, take hints as needed

1. A triangle has base 6 and height 4. Find its area.
½ × base × height.
½ × 6 × 4.
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12.
2. A triangle has base 14 and height 5. Find its area.
½ × 14 × 5.
—
—
35.
3. A triangle has base 9 and height 8. Find its area.
½ × 9 × 8.
—
—
36.
4. A triangle has area 30 and base 10. Find its height.
30 = ½ × 10 × h.
30 = 5h.
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6.
5. A triangle has base 20 and height 3. Find its area.
½ × 20 × 3.
—
—
30.

📝 Topic test — 8 questions

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