Worksheets · Geometry

Pythagorean theorem worksheet for Geometry

Most of these triangles have whole-number sides from common triples, so the answers come out clean. The rest round to the nearest tenth, and the area questions find the missing leg first.

Also taught in Pre-Algebra, at its own level and with its own examples.

Not quite the one you need? Same words, different skill:

Select your difficulty

Pick more than one for a sheet that mixes them.

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

Sigma Prep · sigmaprep.io/worksheets

Name

The Pythagorean Theorem

Date Period

Find each missing length or area. Leave square roots exact unless the question says to round.

  1. Find the missing side

    How long is the side marked x?10x26
  2. Find the hypotenuse of a right triangle whose legs are 60 and 91.
  3. Find the missing side.x3685
  4. Find the length of the side marked x.34x
  5. The triangle is a right triangle. Find x.x3989

  1. Solve Pythagorean word problems

    A hiker walks 8 km north, then 15 km east. How far is the hiker from the start, in a straight line?
  2. A rectangular field is 13 m by 84 m. How long is the path straight across it, corner to corner?
  3. A rectangular sign is 40 in wide and 9 in tall. How long is its diagonal?
  4. A guy wire 65 ft long runs from the top of a pole to a stake 16 ft from the pole's base. How tall is the pole?
  5. A straight staircase rises 20 ft over a level distance of 21 ft. How long is its handrail, end to end?

  1. Find the area with the Pythagorean theorem

    Find the area of the triangle.7424
  2. Find the area.10690
  3. Use the Pythagorean theorem to find the area.7355
  4. Find the area of the triangle.6556
  5. Use the Pythagorean theorem to find the area.9772

  1. Find the side to the nearest tenth

    Find the length x to the nearest tenth.x3.57.7
  2. Find x to the nearest tenth.12.67.4x
  3. Find the missing side x to the nearest tenth.7.86.6x
  4. Find x to the nearest tenth.x8.64.6
  5. Find the missing side x to the nearest tenth.x7.16.4

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

Sigma Prep · sigmaprep.io/worksheets

Name

The Pythagorean TheoremAnswer keyVersion 1

Date Period

Find each missing length or area. Leave square roots exact unless the question says to round.

  1. Find the missing side

    How long is the side marked x?10x2624
  2. Find the hypotenuse of a right triangle whose legs are 60 and 91.109
  3. Find the missing side.x368577
  4. Find the length of the side marked x.34x5
  5. The triangle is a right triangle. Find x.x398980

  1. Solve Pythagorean word problems

    A hiker walks 8 km north, then 15 km east. How far is the hiker from the start, in a straight line?17 km
  2. A rectangular field is 13 m by 84 m. How long is the path straight across it, corner to corner?85 m
  3. A rectangular sign is 40 in wide and 9 in tall. How long is its diagonal?41 in
  4. A guy wire 65 ft long runs from the top of a pole to a stake 16 ft from the pole's base. How tall is the pole?63 ft
  5. A straight staircase rises 20 ft over a level distance of 21 ft. How long is its handrail, end to end?29 ft

  1. Find the area with the Pythagorean theorem

    Find the area of the triangle.7424840
  2. Find the area.106902520
  3. Use the Pythagorean theorem to find the area.73551320
  4. Find the area of the triangle.6556924
  5. Use the Pythagorean theorem to find the area.97722340

  1. Find the side to the nearest tenth

    Find the length x to the nearest tenth.x3.57.78.5
  2. Find x to the nearest tenth.12.67.4x10.2
  3. Find the missing side x to the nearest tenth.7.86.6x4.2
  4. Find x to the nearest tenth.x8.64.69.8
  5. Find the missing side x to the nearest tenth.x7.16.49.6

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

How to do these

The legs of a right triangle are 6 and 8. Find the hypotenuse

  1. Square both legs: 36 and 64.
  2. Add them: 100.
  3. Take the square root.

The answer is 10.

Where students go wrong

Using the theorem to find a leg by adding rather than subtracting. The hypotenuse squared is the total, so finding a leg means taking the other one away from it.

Also called Pythagoras, finding the hypotenuse or missing leg.

What you can put on this worksheet

A missing side, left exact
One leg of a right triangle is 8 and its hypotenuse is 17. Find the other leg. → 15
Problems that take two steps
A rectangle has a diagonal of 39 and a side of 15. Find its perimeter. → 102
Word problems
A hiker walks 9 km north, then 40 km east. How far is the hiker from the start, in a straight line? → 41 km
Area from the hypotenuse and a leg
Find the area. — a right triangle, labeled 130, 66 → 3696
Decimal sides, rounded
Find the missing side x to the nearest tenth. — a right triangle, labeled x, 7.8, 2.6 → 8.2
Split by the altitude: the other piece, or the area
Find x. — a triangle split by its altitude, labeled 37, 15, 9, x → 35

Questions about these worksheets

Yes. Every pythagorean theorem 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 pythagorean theorem 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 two 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 6: a missing side, left exact, problems that take two steps, word problems, area from the hypotenuse and a leg, decimal sides, rounded and split by the altitude: the other piece, or the area. Tick as many as you want and set how many of each, or let it spread them evenly.

Using the theorem to find a leg by adding rather than subtracting. The hypotenuse squared is the total, so finding a leg means taking the other one away from it.