Measurement and Geometry
What you need to know
Expect questions on perimeter, area, surface area, volume, angle relationships, the Pythagorean theorem, similar figures, coordinate geometry, and unit conversion. Know the formulas for rectangles, triangles, circles, and rectangular solids, and know that the sum of angles in a triangle is 180° and in a quadrilateral 360°.
Traps to watch for
- Radius versus diameter: the circle formulas use the radius. If the problem gives the diameter, halve it first.
- Perimeter versus area: perimeter is a length (units), area is squared units. Answer choices often include the wrong one.
- Unit conversion: set up a conversion so unwanted units cancel. Square and cubic units need the conversion factor squared or cubed (1 m = 100 cm, so 1 m² = 10,000 cm²).
- Similar figures: side lengths scale by the factor, but areas scale by the factor squared and volumes by the factor cubed.
- Pythagorean theorem: it applies only to right triangles, and the hypotenuse is always the longest side.
Rule of thumb
Write the formula down before substituting numbers, and label every answer with its unit. If the units do not match what the question asks for, you have found the error.
Worked example
A circular garden has a diameter of 10 ft. Its area is πr² with r = 5, so A = π × 25 ≈ 78.5 ft². Its circumference is πd = 10π ≈ 31.4 ft. Notice the area answer carries square feet and the circumference answer carries feet.