Worksheets · Geometry

Geometric mean worksheet for Geometry

Geometry uses the geometric mean, the square root of a product, in right triangles: the altitude to the hypotenuse is the geometric mean of the two pieces it cuts. Half the sheet finds that altitude from a figure. The other half finds the geometric mean of two numbers in simplest radical form.

Also taught in Algebra 2 and Precalculus, each at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Geometric Mean

Date Period

Answer each question.

  1. Use the geometric mean of two numbers

    Find the geometric mean of 10 and 28.
  2. Find the geometric mean of 14 and 42.
  3. Find the geometric mean of 26 and 9.
  4. Find the geometric mean of 8 and 39.
  5. Find the geometric mean of 18 and 7.
  6. Find the geometric mean of 24 and 36.
  7. Find the geometric mean of 29 and 36.
  8. Find the geometric mean of 22 and 8.
  9. Find the geometric mean of 22 and 20.
  10. Find the geometric mean of 10 and 26.

  1. Use the geometric mean in right triangles

    Find x, the altitude to the hypotenuse.925x
  2. Find the missing piece of the hypotenuse.x1812
  3. The altitude is drawn to the hypotenuse. Find x.28x14
  4. Find the altitude.916x
  5. Find x.25x20
  6. Find x, the altitude to the hypotenuse.49x
  7. Find the altitude.369x
  8. Find x.x2515
  9. Find the altitude.2516x
  10. Find the missing piece of the hypotenuse.x612

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Geometric MeanAnswer keyVersion 2

Date Period

Answer each question.

  1. Use the geometric mean of two numbers

    Find the geometric mean of 10 and 28.270
  2. Find the geometric mean of 14 and 42.143
  3. Find the geometric mean of 26 and 9.326
  4. Find the geometric mean of 8 and 39.278
  5. Find the geometric mean of 18 and 7.314
  6. Find the geometric mean of 24 and 36.126
  7. Find the geometric mean of 29 and 36.629
  8. Find the geometric mean of 22 and 8.411
  9. Find the geometric mean of 22 and 20.2110
  10. Find the geometric mean of 10 and 26.265

  1. Use the geometric mean in right triangles

    Find x, the altitude to the hypotenuse.925x15
  2. Find the missing piece of the hypotenuse.x18128
  3. The altitude is drawn to the hypotenuse. Find x.28x147
  4. Find the altitude.916x12
  5. Find x.25x2016
  6. Find x, the altitude to the hypotenuse.49x6
  7. Find the altitude.369x18
  8. Find x.x25159
  9. Find the altitude.2516x20
  10. Find the missing piece of the hypotenuse.x61224

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Find the geometric mean of 8 and 30

  1. The geometric mean is √(8 × 30) = √240.
  2. 240 = 16 × 15, so √240 = 4√15.

The answer is 415.

Where students go wrong

Inserting means with a common difference. Between 6 and 162 the terms multiply by one ratio: r³ = 162 ÷ 6 = 27, so r = 3 and the means are 18 and 54, not the evenly spaced 58 and 110.

Also called geometric mean, geometric means, inserting geometric means or geometric mean of two numbers.

What you can put on this worksheet

The geometric mean of two numbers
Find the geometric mean of 49 and 9. → 21
Insert geometric means between two numbers
Insert two geometric means between 5 and 320. → 20,  80
The geometric mean in a right triangle
The altitude is drawn to the hypotenuse. Find x. — a right triangle with the altitude drawn to its hypotenuse, labeled x, 9, 12 → 16
Negative ends, three means, fractions: both signs of the ratio
Find the missing terms of the geometric sequence: 625,___,___,___,1 → 125,25,5 or −125,25,−5

Questions about these worksheets

Yes. Every geometric mean sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the geometric mean questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 4: the geometric mean of two numbers, insert geometric means between two numbers, the geometric mean in a right triangle and negative ends, three means, fractions: both signs of the ratio. Tick as many as you want and set how many of each, or let it spread them evenly.

Averaging instead: the numbers halfway between 3 and 81 are arithmetic means. Geometric means multiply by the same number each step, they do not add.