Area of Shapes — SAT Math Explained
The amount of two-dimensional space enclosed within a geometric figure, measured in square units.
The Core Idea
Most area formulas derive from the rectangle formula (length × width). Triangles are half a rectangle; parallelograms use the same base-times-height logic; trapezoids average the two parallel bases.
Key Formulas
A = length × width
A = side²
A = (1/2) × base × height
A = base × height (height is perpendicular, NOT the slant side)
A = (1/2) × (base₁ + base₂) × height
A = πr²
A = (1/2) × perimeter × apothem
Height Clarification
Height is always the perpendicular distance — for triangles and parallelograms, it may not be a visible side. You may need to use the Pythagorean theorem to find it.
Composite Shapes
Break the shape into recognizable simpler shapes
Calculate the area of each part
Add areas (or subtract if one shape is cut out from another)
Common Errors to Avoid
Using the slant height instead of the perpendicular height
Forgetting the 1/2 in the triangle area formula
Using radius² without π for circle area
Practice: Area of Shapes
5 SAT-style questions. Select your answer and get an instant explanation.
Rectangle 7 by 11. Area?
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