MathGeometry & TrigonometryMedium frequency
SAT Math: Area of Triangles and Polygons
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What you need to know
The concept, explained
- 1
Triangle area: A = (1/2) × base × height. The height must be perpendicular to the base.
- 2
Parallelogram area: A = base × height (same perpendicular height principle).
- 3
Trapezoid area: A = (1/2)(b₁ + b₂) × h, where b₁ and b₂ are the parallel sides.
- 4
For composite figures, decompose into simpler shapes and add or subtract areas.
- 5
When the height is not given explicitly, you may need the Pythagorean theorem to find it.
Common mistakes
- ✗ Using a slant side as the height — the height must be perpendicular to the base.
- ✗ Forgetting the (1/2) factor in the triangle formula and computing base × height.
Try a sample question
SAT-style practice
A trapezoid has parallel sides of length 6 and 10, and a height of 4. What is its area?
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