GED Geometry Practice

Geometry on the GED is measurement, not proof. You will not be asked to prove a theorem; you will be asked to pick the right formula and use it cleanly.

Question 1 of 23

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A shipping box is a cube 1.5 feet on each side. How many square feet of cardboard cover its outside?

Geometry study guide

GED geometry is about measurement: how long, how much surface, how much space. The formula sheet gives you the formulas, so the skill being tested is choosing the right one and using the right measurements in it. This guide shows how to make that choice quickly.

Perimeter and area of flat shapes

Perimeter is the distance around a shape, measured in plain units such as feet. Area is the space inside, measured in square units such as square feet. When a problem mentions fencing, trim, or a border, it wants perimeter. When it mentions carpet, paint, tile, or sod, it wants area.

For a rectangle, area is length × width. For a triangle, area is ½ × base × height, where the height is perpendicular to the base, not the slanted side. A parallelogram is base × height. A trapezoid is ½ × (base₁ + base₂) × height.

Worked example

A room is 14 ft by 11 ft. Carpet costs $3.50 per square foot. What does it cost to carpet the room?

  1. Carpet covers the floor, so use area: 14 × 11 = 154 square feet.
  2. Multiply by the price: 154 × 3.50 = $539.

Circles

The radius runs from the center to the edge. The diameter runs all the way across and is twice the radius. Circumference, the distance around, is 2πr or πd. Area is πr². Both formulas are on the sheet, but they need the radius, and the most common trap is a problem that gives the diameter.

Unless the question says otherwise, use the π key on the calculator or 3.14. Check the answer choices: if they are written with π, leave π in your answer.

Worked example

A circular table top has a diameter of 6 feet. What is its area, to the nearest square foot?

  1. Convert diameter to radius: 6 ÷ 2 = 3 feet.
  2. Area = π × 3² = 9π.
  3. 9 × 3.14 ≈ 28.3, so about 28 square feet.

Volume and surface area of solids

Volume is the space inside a solid, in cubic units. A rectangular prism is length × width × height. A cylinder is πr²h, the area of the circular base times the height. Cones and pyramids hold one third of the matching prism or cylinder, which is why their formulas include ⅓.

Surface area is the total area of all the outside faces. It answers questions about wrapping, painting the outside, or the material needed to build a box. When in doubt, sketch the faces and add their areas.

Worked example

A cylindrical tank has radius 2 m and height 5 m. How many cubic meters of water does it hold?

  1. Volume = πr²h = π × 2² × 5.
  2. That is 20π cubic meters.
  3. 20 × 3.14 ≈ 62.8 cubic meters.

The Pythagorean theorem

In any right triangle, a² + b² = c², where c is the hypotenuse, the longest side and the one opposite the right angle. Use it when a problem has a right angle and asks for a missing side: a ladder against a wall, the diagonal of a rectangle, or the straight-line distance between two points.

Watch which side is missing. If you need a leg rather than the hypotenuse, you subtract: a² = c² − b². A few whole-number triples come up often, such as 3-4-5, 5-12-13, and 8-15-17, and multiples of them like 6-8-10.

Worked example

A 13-foot ladder leans against a wall with its base 5 feet from the wall. How high up the wall does it reach?

  1. The ladder is the hypotenuse: c = 13. One leg is 5.
  2. Missing leg: a² = 13² − 5² = 169 − 25 = 144.
  3. a = 12 feet.

Composite shapes and scale

A composite shape is two or more simple shapes joined together, such as a rectangle with a semicircle on one end. Split it into pieces, find each area, and add. If a piece is cut out, subtract it instead.

Scale drawings and similar figures use proportions. If a map scale is 1 inch to 20 miles, 3.5 inches is 70 miles. If two shapes are similar with a scale factor of 3, their lengths differ by 3, their areas by 3² = 9, and their volumes by 3³ = 27.

Angles and polygons

Angle questions on the GED rarely need a formula sheet. They depend on a few facts about how angles fit together. A straight line makes 180°, so two angles that sit side by side on a line are supplementary and add to 180°. Two angles that form a right angle are complementary and add to 90°. A full turn around a point is 360°.

When two straight lines cross, they make four angles. The angles directly across from each other are vertical angles, and they are always equal. The angles next to each other are supplementary. So if you know one of the four angles, you know all of them: two equal that angle and two equal 180° minus it.

The angles inside any triangle add to 180°. A problem may give two angles and ask for the third, or describe the angles in words, such as one angle twice another. Write each angle in terms of one variable, set the sum equal to 180, and solve.

For a polygon with n sides, the interior angles add to (n − 2) × 180°, because the shape can be split into n − 2 triangles. In a regular polygon all angles are equal, so divide that total by n to get one angle. There is also a shortcut through the outside: the exterior angles of any polygon add to 360°, and each exterior angle is 180° minus the interior angle next to it.

  • Supplementary angles add to 180°, complementary angles add to 90°.
  • Vertical angles are equal.
  • Triangle angles add to 180°; polygon angles add to (n − 2) × 180°.

Worked example

A sign is shaped like a regular octagon. What is the measure of each interior angle?

  1. An octagon has 8 sides, so n = 8.
  2. Sum of the interior angles: (8 − 2) × 180° = 6 × 180° = 1,080°.
  3. The polygon is regular, so all 8 angles are equal: 1,080° ÷ 8 = 135°.
  4. Check with exterior angles: 360° ÷ 8 = 45°, and 180° − 45° = 135°.

Checklist before test day

Practice until each of these takes under a minute.

  • Decide whether a word problem wants perimeter, area, or volume.
  • Convert a diameter to a radius before using a circle formula.
  • Use the perpendicular height, not a slanted side, for triangle area.
  • Find a missing leg or hypotenuse with a² + b² = c².
  • Split a composite figure into rectangles, triangles, and circle parts.
  • Keep units consistent, converting inches to feet before you compute.

Geometry practice set 1: 23 questions with answers

Work each question on paper first, then open the answer to check your reasoning.

  1. 1.A shipping box is a cube 1.5 feet on each side. How many square feet of cardboard cover its outside?

    1. A.13.5 sq ft
    2. B.3.375 sq ft
    3. C.9 sq ft
    4. D.2.25 sq ft
    Show answer

    Answer: A. 13.5 sq ft

    Each face is 1.5 × 1.5 = 2.25 square feet, and a cube has 6 faces, so 6 × 2.25 = 13.5. Choice 3.375 is the volume, 1.5³.

  1. 2.A square pyramid has a base 6 m on each side. Each triangular face has a slant height of 5 m. What is the total surface area?

    1. A.60 m²
    2. B.66 m²
    3. C.96 m²
    4. D.156 m²
    Show answer

    Answer: C. 96 m²

    The base is 6 × 6 = 36 m², and each of the 4 triangles is ½ × 6 × 5 = 15 m², adding 60 m². The total is 96 m². Choice 60 m² leaves out the square base.

  1. 3.A running track is a rectangle 100 m long with a semicircle on each short end. Each semicircle has a diameter of 60 m. To the nearest meter, how long is one lap around the outside edge? (Use π ≈ 3.14.)

    1. A.508 m
    2. B.294 m
    3. C.577 m
    4. D.388 m
    Show answer

    Answer: D. 388 m

    The two semicircles together make one full circle with circumference 3.14 × 60 = 188.4 m. Add the two straight sides, 2 × 100 = 200 m, for about 388 m. Choice 508 m also counts the 60 m short sides, which are inside the track.

  1. 4.A wall is 12 feet wide and 8 feet tall. It has a door 3 feet by 7 feet and a window 4 feet by 3 feet. How many square feet of wall need paint?

    1. A.63 sq ft
    2. B.96 sq ft
    3. C.75 sq ft
    4. D.129 sq ft
    Show answer

    Answer: A. 63 sq ft

    The wall is 12 × 8 = 96 square feet. Subtract the door (21) and the window (12) to get 63 square feet. Choice 75 subtracts only the door.

  1. 5.A map scale shows that 2 centimeters represent 15 kilometers. Two towns are 9 centimeters apart on the map. How far apart are they?

    1. A.135 km
    2. B.67.5 km
    3. C.30 km
    4. D.22.5 km
    Show answer

    Answer: B. 67.5 km

    Each centimeter is 15 ÷ 2 = 7.5 km, so 9 cm is 9 × 7.5 = 67.5 km. Choice 135 km uses 15 km per centimeter and ignores the 2.

  1. 6.Two picture frames are similar rectangles. The smaller is 8 inches by 10 inches, and each side of the larger is 1.5 times as long. What is the area of the larger frame?

    1. A.120 sq in
    2. B.80 sq in
    3. C.180 sq in
    4. D.270 sq in
    Show answer

    Answer: C. 180 sq in

    The larger frame is 12 by 15 inches, so its area is 180 square inches, which is 1.5² = 2.25 times the original 80. Choice 120 multiplies the area by 1.5 instead of 1.5².

  1. 7.The sides of one triangle are 5, 7, and 9 inches. A similar triangle has a shortest side of 12.5 inches. How long is its longest side?

    1. A.16.5 inches
    2. B.18 inches
    3. C.22.5 inches
    4. D.20 inches
    Show answer

    Answer: C. 22.5 inches

    The scale factor is 12.5 ÷ 5 = 2.5, so the longest side is 9 × 2.5 = 22.5 inches. Choice 16.5 adds 7.5 to the side instead of multiplying by the scale factor.

  1. 8.A logo is shaped like a regular pentagon. What is the measure of each interior angle?

    1. A.108°
    2. B.72°
    3. C.540°
    4. D.120°
    Show answer

    Answer: A. 108°

    The interior angles of a pentagon add to (5 − 2) × 180 = 540°, so each of the five equal angles is 540 ÷ 5 = 108°. Choice 72° is the exterior angle, 360 ÷ 5.

  1. 9.A circular rug has a circumference of 18.84 feet. What is its radius? (Use π ≈ 3.14.)

    1. A.6 feet
    2. B.3 feet
    3. C.9.42 feet
    4. D.2.45 feet
    Show answer

    Answer: B. 3 feet

    Circumference is 2πr, so r = 18.84 ÷ 6.28 = 3 feet. Choice 6 feet is the diameter, found by dividing by π alone.

  1. 10.A bicycle wheel has a diameter of 26 inches. About how far does the bike travel in 50 full turns of the wheel? (Use π ≈ 3.14.)

    1. A.About 2,041 inches
    2. B.About 4,082 inches
    3. C.About 1,300 inches
    4. D.About 8,164 inches
    Show answer

    Answer: B. About 4,082 inches

    One turn covers the circumference: 3.14 × 26 ≈ 81.64 inches, and 50 × 81.64 = 4,082 inches. Choice About 2,041 inches multiplies π by the radius instead of the diameter.

  1. 11.A pizza with a 14-inch diameter costs $15.40. To the nearest cent, what is the price per square inch? (Use π ≈ 3.14.)

    1. A.$0.35
    2. B.$0.03
    3. C.$0.10
    4. D.$1.10
    Show answer

    Answer: C. $0.10

    The radius is 7, so the area is 3.14 × 49 ≈ 153.86 square inches, and $15.40 ÷ 153.86 ≈ $0.10. Choice $0.03 uses 14 as the radius, which makes the area four times too large.

  1. 12.Point A is at (−2, −3) and point B is at (4, 5) on a coordinate grid. What is the distance between them?

    1. A.14
    2. B.10
    3. C.6
    4. D.100
    Show answer

    Answer: B. 10

    The horizontal change is 4 − (−2) = 6 and the vertical change is 5 − (−3) = 8. Distance = √(6² + 8²) = √100 = 10. Choice 14 adds the two changes instead of using the Pythagorean theorem.

  1. 13.A rectangular park is 90 meters long. A straight diagonal path across it is 150 meters long. How wide is the park?

    1. A.120 meters
    2. B.175 meters
    3. C.60 meters
    4. D.240 meters
    Show answer

    Answer: A. 120 meters

    The path is the hypotenuse, so width² = 150² − 90² = 22,500 − 8,100 = 14,400, and the width is 120 meters. Choice 175 meters adds the squares, which treats the path as a leg.

  1. 14.A garden bed is a rectangle 8 ft by 5 ft with a right triangle attached along one 5-ft end. The triangle’s legs are 5 ft and 6 ft. What is the total area of the bed?

    1. A.70 square feet
    2. B.48 square feet
    3. C.55 square feet
    4. D.43 square feet
    Show answer

    Answer: C. 55 square feet

    The rectangle is 8 × 5 = 40 square feet and the triangle is ½ × 5 × 6 = 15 square feet, for 55 in all. Choice 70 square feet forgets the ½ in the triangle formula.

  1. 15.An L-shaped patio is a 16 ft by 12 ft rectangle with a 6 ft by 5 ft rectangle removed from one corner. Edging will go around the whole outside of the patio. How many feet of edging are needed?

    1. A.45 feet
    2. B.162 feet
    3. C.67 feet
    4. D.56 feet
    Show answer

    Answer: D. 56 feet

    Cutting out a corner does not change the perimeter: the two new edges (6 ft and 5 ft) replace the two pieces of the outer edge that were removed. So the perimeter is 2(16 + 12) = 56 feet. Choice 162 feet is the area in square feet, not a length.

  1. 16.Each interior angle of a regular polygon measures 140°. How many sides does the polygon have?

    1. A.7
    2. B.9
    3. C.12
    4. D.6
    Show answer

    Answer: B. 9

    Each exterior angle is 180° − 140° = 40°, and the exterior angles of any polygon add to 360°, so there are 360 ÷ 40 = 9 sides. Choice 7 would give interior angles of about 128.6°, not 140°.

  1. 17.A swimming pool is 30 ft long, 15 ft wide, and 4 ft deep. One cubic foot holds about 7.5 gallons. About how many gallons does the pool hold when full?

    1. A.1,800 gallons
    2. B.6,750 gallons
    3. C.3,375 gallons
    4. D.13,500 gallons
    Show answer

    Answer: D. 13,500 gallons

    Volume = 30 × 15 × 4 = 1,800 cubic feet, and 1,800 × 7.5 = 13,500 gallons. Choice 1,800 gallons stops at cubic feet and skips the conversion.

  1. 18.A model car is built at a scale of 1 to 24. The model is 7.5 inches long. How long is the real car?

    1. A.15 feet
    2. B.180 feet
    3. C.18 feet
    4. D.3.2 feet
    Show answer

    Answer: A. 15 feet

    Multiply by 24: 7.5 × 24 = 180 inches. Divide by 12 to change to feet: 180 ÷ 12 = 15 feet. Choice 180 feet skips the change from inches to feet.

  1. 19.A cylindrical oatmeal container has a radius of 2 inches and a height of 7 inches. It has a bottom but no lid. To the nearest square inch, what is its outside surface area? (Use π ≈ 3.14.)

    1. A.113 square inches
    2. B.100 square inches
    3. C.88 square inches
    4. D.126 square inches
    Show answer

    Answer: B. 100 square inches

    The side is 2πrh = 2(3.14)(2)(7) = 87.92, and the bottom is πr² = 3.14(4) = 12.56, for a total of about 100 square inches. Choice 113 square inches includes a lid the container does not have.

  1. 20.A cube-shaped storage ottoman has a total surface area of 54 square feet. How long is each edge?

    1. A.9 feet
    2. B.6 feet
    3. C.4.5 feet
    4. D.3 feet
    Show answer

    Answer: D. 3 feet

    A cube has 6 equal faces, so each face is 54 ÷ 6 = 9 square feet and each edge is √9 = 3 feet. Choice 9 feet is the area of one face, not the edge length.

  1. 21.Two triangles are similar. The smaller has a base of 4 cm and an area of 10 cm². The matching base of the larger triangle is 12 cm. What is the area of the larger triangle?

    1. A.90 cm²
    2. B.30 cm²
    3. C.120 cm²
    4. D.40 cm²
    Show answer

    Answer: A. 90 cm²

    The scale factor is 12 ÷ 4 = 3, and areas grow by the square of the scale factor: 10 × 3² = 90 cm². Choice 30 cm² multiplies the area by 3, as if it were a length.

  1. 22.A photo 4 inches wide and 6 inches tall is enlarged so its width is 10 inches. If the shape stays the same, what is the new height?

    1. A.12 inches
    2. B.24 inches
    3. C.15 inches
    4. D.9 inches
    Show answer

    Answer: C. 15 inches

    The scale factor is 10 ÷ 4 = 2.5, so the height is 6 × 2.5 = 15 inches. Choice 12 inches adds 6 inches to the height, as was added to the width, which distorts the shape.

  1. 23.A fish tank is 30 inches long, 12 inches wide, and 16 inches tall. It is filled with water to 2 inches below the top. What is the volume of the water?

    1. A.5,760 cubic inches
    2. B.720 cubic inches
    3. C.4,320 cubic inches
    4. D.5,040 cubic inches
    Show answer

    Answer: D. 5,040 cubic inches

    The water is 16 − 2 = 14 inches deep, so 30 × 12 × 14 = 5,040 cubic inches. Choice 5,760 cubic inches is the volume of the whole tank.

More practice sets

Geometry has 2 practice sets. None of these questions appear in the full practice tests.

The shapes that actually appear on the GED

Rectangles, triangles, circles, rectangular prisms, cylinders, and cubes cover the large majority of GED geometry questions. For each, you should be able to compute area or surface area and volume without hesitating over which dimension goes where. Cones, pyramids, and spheres appear occasionally, and their formulas are on the reference sheet.

The Pythagorean theorem is a reliable presence, often disguised inside a word problem about a ladder against a wall or the diagonal of a rectangular yard. When a right angle and two side lengths appear together, that theorem is almost always the intended route.

The radius and diameter trap in GED geometry

More circle questions are missed for this reason than any other: the problem states the diameter, and the formula wants the radius. Before you compute anything with a circle, write down r explicitly. If the question gives 14 inches across, write r = 7 on your scratch board first.

The related trap is units. Area answers are in square units, volume in cubic units, and the answer choices will include a correct number attached to the wrong unit. Check the unit last, every time.

Similar figures and scale on the GED

Similar-figure questions give you two shapes with the same angles and different sizes, then ask for a missing length. Find the scale factor by dividing one pair of matching sides, then apply that same factor to the side you need. Set it up as a proportion if that feels safer. Both methods score the same.

Frequently asked questions

Do I have to memorize geometry formulas for the GED?
No. A formula reference sheet is available throughout the Mathematical Reasoning test. Practice choosing and applying formulas rather than memorizing them.
Is trigonometry on the GED?
Basic right-triangle relationships may appear, but the test does not require sine, cosine, and tangent the way a college algebra course would.