Geometry and Measurement on the GED Math Test

That is where the marks go missing. A student who knows the cylinder formula perfectly can still put the diameter where the radius belongs and get an answer four times too big, and that wrong answer will be sitting among the choices. The set below is built around those specific slips.

Geometry sits inside the "quantitative problem solving in measurement" reporting category, which GED Testing Service weights at about 20% of the test. It shares that category with data and statistics, so expect roughly four to six geometry questions on a full test.

Skills in this set: Volume of a cylinder · Pythagorean theorem · Area of a rectangle or square · Area of a triangle · Area of a parallelogram · Area of a trapezoid · Area and circumference of a circle · Perimeter in context · Volume of a rectangular prism · Finding a cylinder's height from its volume · Volume of a cone · Volume of a sphere · Volumes of a prism, a pyramid and a cone · Surface area of a rectangular prism · Surface area of a cylinder · Pythagorean theorem in context · Area of a composite figure · Scale drawings and actual measurements

What the test asks

The Assessment Guide for Educators lists the geometry indicators as Q.4.a through Q.5.f. In plain terms: perimeter and area of squares, rectangles, triangles, parallelograms, trapezoids and circles (Q.4.a, Q.4.c); shapes made of more than one of those, where you add or subtract areas (Q.4.d); the Pythagorean theorem for a missing side of a right triangle (Q.4.e); scale drawings and scale factors (Q.4.b); and volume and surface area of rectangular prisms, cylinders, cones, pyramids and spheres (Q.5.a through Q.5.f).

Two things the guide says matter for how you study. The first is that questions come in real contexts: a garden to fence, a can to label, a tank to fill, a ramp to build. The second is that the test is written to reward choosing the right formula and substituting carefully, more than it rewards arithmetic. The numbers are usually friendly if you set the problem up correctly.

You get the on-screen calculator for almost all of these. The exception is the short no-calculator section at the start of the test, where a geometry item, if one appears, will use numbers you can handle by hand: a 6 by 8 rectangle, a triangle with base 10 and height 4.

The mistakes this set is built to catch

Each wrong answer in the practice set is the result of one specific slip, and the explanation names it. These are the ones that come up most in this topic.

A worked example

How to practice it

1. Before you calculate anything, write down what each letter in the formula equals: r = 3, h = 10. This takes five seconds and catches the diameter-for-radius slip, which is the most expensive mistake in this topic.
2. Learn the three relationships the sheet does not spell out: triangle equals half a rectangle, cone equals a third of a cylinder, pyramid equals a third of a prism. They make the fractions impossible to forget and let you rebuild a forgotten formula from a remembered one.
3. Estimate before you compute. A cylinder 3 feet across and 10 feet tall should hold something in the low hundreds of cubic feet, not in the thousands. If your answer is off by a factor of four or ten, you will notice.
4. For a shape made of several pieces, sketch it and split it into rectangles, triangles and half-circles before you touch a formula. Find each piece's area separately and add, or subtract a cut-out from a whole. The arithmetic is easy once the pieces are named.