Math Section · Study Guide
The Math section tests perimeter, area, and circumference — by hand, no calculator. Learn the three shapes that show up most, then lock in the formulas with worked examples.
A rectangle has four right angles. Opposite sides are equal. Hover the labels below to highlight each dimension.
Perimeter = 2L + 2W = 2(12) + 2(8) = 40 in
Area = L × W = 12 × 8 = 96 in²
For area, you need the base and the perpendicular height — the straight-line distance from the base to the opposite vertex. The dashed line shows the height.
Area = ½ × b × h = ½ × 14 × 10 = 70 in²
The radius goes from the center to the edge. The diameter is twice the radius. On the test, use π = 3.14 unless told otherwise.
Circumference = 2πr = 2 × 3.14 × 7 = 43.96 in
Area = πr² = 3.14 × 7² = 153.86 in²
Example 1
A rectangular pipe trench is 24 feet long and 3 feet wide. What is the area of the trench opening?
Identify the formula: A = L × W
Plug in: A = 24 × 3
Solve: A = 72 ft²
Tip: Watch the units. If length is in feet and width is in inches, convert first. The test loves mixing units to trip you up.
Example 2
A circular pipe has an outer diameter of 10 inches. What is the cross-sectional area of the pipe?
Find the radius: r = d ÷ 2 = 10 ÷ 2 = 5 in
Apply the formula: A = πr² = 3.14 × 5²
Solve: A = 3.14 × 25 = 78.5 in²
Tip: The test gives you a diameter but the formula uses radius. Always divide by 2 first. This is the most common geometry mistake on the exam.
| Shape | Formula | What to Remember |
|---|---|---|
| Rectangle — Perimeter | P = 2L + 2W | Add all four sides. Two lengths + two widths. |
| Rectangle — Area | A = L × W | Length times width. Square units (ft², in²). |
| Triangle — Area | A = ½ × b × h | Half a rectangle. Height must be perpendicular to base. |
| Circle — Circumference | C = 2πr | Distance around. Also equals πd. Use π = 3.14. |
| Circle — Area | A = πr² | Square the radius first, then multiply by π. |
Lock in these formulas with timed practice problems that match the real test format — pencil and paper, no calculator.