Area and Volume
Calculating area, perimeter, and volume, including scale factors and composite shapes
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Your workbook starts day one with a diagnostic that finds your blind spots, then builds targeted practice around the patterns actually costing you points.
You get a shape and its dimensions. Plug into the right formula, or work backward to find a missing measurement.
Why this matters
Area and Volume questions look simple, but the SAT packs them with small catches — using diameter instead of radius, forgetting the one-third in a cone formula, confusing perimeter with area. Students who treat this as "just formulas" walk right into those pitfalls.
The five patterns
Formula Calculation
Plug given dimensions into the right formula and simplify. Rectangles, triangles, circles, cylinders, cones, spheres — know them cold.
›Inverse Calculation
You get the area or volume and work backward to find a missing dimension. Same formulas, opposite direction.
›Scaling & Proportionality
When you double a side, area quadruples and volume multiplies by eight. These questions test whether you understand how dimensions scale.
›Multi-Step Composite
Combine multiple calculations — find an intermediate value first, then use it in a second formula, or break a complex shape into simpler pieces.
›Geometric Algebra
Dimensions are given as variables or expressions. Set up an equation from the geometric formula and solve for the unknown.