Geometry and Measurement
What this domain covers
Geometry and Measurement tests perimeter, circumference, area, volume, and surface area of common figures, plus the Pythagorean theorem, angle relationships, similar figures, scale drawings, and unit conversions within the customary and metric systems. You should be able to break a composite shape into rectangles, triangles, and semicircles, and to choose the correct formula without being handed a formula sheet.
Formulas worth memorizing
Area of a rectangle is length times width; of a triangle, one-half base times height; of a circle, pi times radius squared. Circumference is pi times diameter. Volume of a rectangular prism is length times width times height. In any triangle the angles total 180 degrees, and a straight line totals 180 degrees as well.
Traps to watch for
- Mixing radius and diameter; the radius is half the diameter.
- Reporting area in linear units or perimeter in square units.
- Using the slant edge where the perpendicular height is required.
- Converting in the wrong direction - multiply when going to a smaller unit, divide when going to a larger one.
- Double-counting shared sides when finding the perimeter of a composite figure.
Worked example
A circle has a diameter of 10 inches. Its radius is 5 inches, so the area is pi × 5² ≈ 3.14 × 25 = 78.5 square inches, and the circumference is 3.14 × 10 = 31.4 inches. Rule of thumb: sketch the figure, label every given measure, and write the unit on every answer.