Where this sits. This is one of the four shape, data, and chance families — the middle ground, where the formula sheet does most of the remembering and your job is choosing the right formula. Every family page on this site has the same eight parts, in the same order, so once you know the shape of one you know the shape of all of them. Where a part is empty, it says so.
DrillsTwenty drills for this family, one skill each, ten problems at a timeGo to the drills ↓Perimeter and area of rectangles, triangles, and parallelograms; circles — radius, diameter, circumference, area, with π; volume of boxes, cylinders, cones, and spheres; angles on a line, angles where two lines cross, and the three angles of a triangle; the Pythagorean theorem for the missing side of a right triangle; and similar figures, where two shapes have the same shape but not the same size.
Every formula is on the sheet they hand you. Recognizing which shape you are looking at is not. That is the whole of the work in this family, and it is why we build it from pictures rather than from the formula list.
What the test asks in this family
- PerimeterQuiz 27
- Area of rectangles, triangles, and parallelogramsQuiz 27
- Figures made of two shapes joinedQuiz 27
- What happens to area when the sides doubleQuiz 27
- Area of a trapezoidQuiz 37
- Radius, diameter, and circumferenceCircles and Equations
- Area of a circle, and where π comes fromCircles and Equations
- The Pythagorean theoremThe Third Side
- Volume of boxes, prisms, cylinders, cones, pyramids, spheresQuiz 35
- Surface areaQuiz 35
- Angles on a line, at a crossing, and in a triangleQuiz 36
- Similar figuresQuiz 37
All 12 have something on this site.
Seven questions across the biggest family on the test. Every formula here is on the sheet they hand you — the work is choosing the right one. Type an answer and press Check.
- A rectangle is 9 cm by 4 cm. What is its perimeter? 26 cm. Perimeter is the walk all the way around: 9 + 4 + 9 + 4 = 26. The formula on the sheet, P = 2l + 2w, says the same thing more briefly. Perimeter answers are in plain units, because you only added lengths together.
- The same rectangle, 9 cm by 4 cm. What is its area? 36 square cm. Area is the fill, not the walk: 9 × 4 = 36. Two shapes can have the same perimeter and different areas, which is why the two questions have to be told apart before you reach for a formula.
- A triangle has a base of 10 inches and a height of 6 inches. What is its area? 30 square inches. The formula is A = ½bh, so ½ × 10 × 6 = 30. The half is there because a triangle is exactly half of the rectangle you could draw around it. Forgetting the half gives 60, which is that whole rectangle.
- A circle has a radius of 5. What is its circumference? Use π ≈ 3.14. 31.4. Circumference is the distance around: C = 2πr, so 2 × 3.14 × 5 = 31.4. The radius reaches from the center to the edge; the diameter crosses the whole circle and is twice the radius. Using 5 as the diameter by mistake halves the answer.
- The same circle, radius 5. What is its area? Use π ≈ 3.14. 78.5. Area is A = πr², so 3.14 × 25 = 78.5. Square the radius first, then multiply by π — squaring the whole of 3.14 × 5 instead is the usual slip. Area answers are always in square units.
- A right triangle has legs of 9 and 12. How long is the hypotenuse? 15. The Pythagorean theorem, a² + b² = c², is on the sheet: 81 + 144 = 225, and the square root of 225 is 15. The hypotenuse is always the side opposite the right angle and always the longest — if your answer is shorter than a leg, you have put a number in the wrong place.
- A box measures 4 by 3 by 5. What is its volume? 60 cubic units. Volume of a box is length × width × height: 4 × 3 × 5 = 60. You multiplied three lengths together, so the answer is in cubic units. Volume formulas for cylinders, cones, pyramids and spheres are all on the sheet as well.
Missed one? Quiz 27 in Learn it covers perimeter and area and Quiz 35 covers volume and surface area. Circles and Equations under Work it by hand takes the circle apart, and The Third Side under On paper is seventeen Pythagoras problems with the key behind one click. Quiz 36 covers angles, and Quiz 37 similar figures and the trapezoid. Every part of this family now has a lesson.
Want more than these seven questions? Flyover I asks about all fourteen families in one sitting and ends in a grid that says where to start; Flyover II asks them again later, with different questions, so you can see what has moved.
- Quiz 27Perimeter and AreaRectangles, triangles, and parallelograms: the distance around and the space inside.
- Quiz 35What Fits InsideVolume and surface area: boxes, cans, cones, pyramids and spheres, and how to read the formula sheet they hand you.
- Quiz 36Where Two Lines MeetAngles on a line, at a crossing, across a pair of parallel lines, and inside a triangle. Almost no arithmetic, and four pictures worth drawing.
- Quiz 37Same Shape, Different SizeSimilar figures, scale factor, the shadow problem, what happens to area when you scale — and the trapezoid, reached by cutting the top off a triangle.
Four quizzes, and with them this family is complete: every topic listed above now has a lesson. The Formula Sheet has every geometry formula the test gives you, the two pages below teach the circle and the Pythagorean theorem in more depth, and Diagnostic 3 will make five more problems of any kind here that you get wrong.
Twenty short drills, one skill each, in order. Each starts with two worked examples, then gives you ten problems (or five) and the reasoning for every answer. Each one prints, with the answer key on the last page. When you get all ten right, or all five right twice in a row, the drill gets a check mark on the Drills page.
- 7.01Name the angle: acute, right, obtuse, straight
- 7.02Angles that add to 90° and to 180°
- 7.03Vertical angles, and parallel lines crossed by a line
- 7.04The three angles of a triangle
- 7.05Perimeter of rectangles, triangles and other polygons
- 7.06Area of rectangles and squares
- 7.07Area of triangles
- 7.08Area of parallelograms and trapezoids · calculator allowed
- 7.09Circles: radius, diameter, circumference · calculator allowed
- 7.10Area of a circle · calculator allowed
- 7.11Shapes made of shapes: area and perimeter · calculator allowed
- 7.12Pythagorean theorem: find the hypotenuse · calculator allowed
- 7.13Pythagorean theorem: find a leg · calculator allowed
- 7.14Volume of boxes and cubes · calculator allowed
- 7.15Volume of cylinders · calculator allowed
- 7.16Volume of cones, pyramids and spheres · calculator allowed
- 7.17Surface area of boxes and cylinders · calculator allowed
- 7.18Similar figures: the scale factor and a missing side · calculator allowed
- 7.19What scaling does to area and volume · calculator allowed
- 7.20Pick the right formula from the formula sheet
- Circles and Equations · nine rooms. The first three take an equation apart and put it back together, starting from the times tables. Then the parts of a circle, the edge unrolled to see where π comes from, a walk around a park against the path through the middle, and area. Ends with practice.
- The Third Side · the Pythagorean theorem, on paper: which side is the hypotenuse and why that is where the mistakes happen, two worked examples, then seventeen problems in four parts. Answer key behind one click. Made to print.
- Khan Academy, math · free videos and practice. Search it for area and perimeter, volume, circles, Pythagorean theorem, angles. These are the clips we start from in class.
- Math Antics · short, plain videos on the basics.
- Light & Salt Learning · free GED classes online, with playlists by topic.
- Get Sum Math · GED math on video, one topic at a time.
- Kaplan GED Test Prep and the McGraw-Hill Mathematical Reasoning Workbook · look up geometry in the contents of either.
On to data, graphs, and statistics. It is a change of subject but not of difficulty: the formula sheet helps less there, and reading the graph correctly is most of the question.