Solve problems involving perimeter and area of plane figures. | Area and volume | SAT Math

Perimeter adds edges; area measures the inside, and composite shapes are often split and recombined.

Core Idea

Perimeter adds up all the outer edges; area counts the square units inside. For composite shapes, break them into rectangles, triangles, or circles and combine.

Understanding

Rule: Perimeter adds edges; area counts interior square units.

Perimeter is the outside boundary.
Area uses the matching shape formula.
Composite figures usually need you to split, add, or subtract.

If the question names a shaded region, subtraction is usually the move.

Step by Step

Identify the shape(s) involved — look for rectangles, triangles, circles, or combinations.
Write down the matching formula and note every dimension the problem gives you.
For composite figures, split into simple shapes, calculate each piece, then add or subtract as needed.
Check units: if the answer asks for square feet but dimensions are in inches, convert before multiplying.

Misconceptions

Using diameter instead of radius in $𝜋 𝑟 2$ — this gives 4 times the correct area.
Forgetting to halve the base × height product for a triangle.
Assuming a missing side of an irregular shape equals a nearby labeled side without checking.

Question

Worked Example

A rectangular garden measures 12 feet by 8 feet. A circular fountain with a diameter of 4 feet sits in the center. What is the area of the garden not covered by the fountain, in square feet?

Select an answer to see the explanation