Worksheets · Precalculus

Heron's formula worksheet for Precalculus

Precalculus uses Heron's formula next to the law of cosines and the sine area formula, as the tool for when only the three sides are known. Answers are expected in exact form, so the product under the root is factored and simplified rather than rounded.

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

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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

Heron's Formula

Date Period

Use Heron's formula.

  1. Find the area of a triangle with sides 6,7 and 12. Give an exact answer.
  2. Find the area of a triangle with sides 9,11 and 14. Give an exact answer.
  3. Find the area of a triangle with sides 9,12 and 13. Give an exact answer.
  4. Find the area of a triangle with sides 5,10 and 13. Give an exact answer.
  5. Find the area of a triangle with sides 6,6 and 9. Give an exact answer.
  6. Find the area of a triangle with sides 9,9 and 13. Give an exact answer.
  7. Find the area of a triangle with sides 7,7 and 12. Give an exact answer.
  8. Find the area of a triangle with sides 6,10 and 11. Give an exact answer.
  9. Find the area of a triangle with sides 7,9 and 14. Give an exact answer.
  10. Find the area of a triangle with sides 5,11 and 11. Give an exact answer.
  11. Find the area of a triangle with sides 5,14 and 15. Give an exact answer.
  12. Find the area of a triangle with sides 5,8 and 9. Give an exact answer.
  13. Find the area of a triangle with sides 3,10 and 11. Give an exact answer.
  14. Find the area of a triangle with sides 5,6 and 9. Give an exact answer.
  15. Find the area of a triangle with sides 3,14 and 15. Give an exact answer.
  16. Find the area of a triangle with sides 4,6 and 6. Give an exact answer.
  17. Find the area of a triangle with sides 9,11 and 13. Give an exact answer.
  18. Find the area of a triangle with sides 4,9 and 11. Give an exact answer.
  19. Find the area of a triangle with sides 6,14 and 14. Give an exact answer.
  20. Find the area of a triangle with sides 8,9 and 13. Give an exact answer.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Heron's FormulaAnswer keyVersion 2

Date Period

Use Heron's formula.

  1. Find the area of a triangle with sides 6,7 and 12. Give an exact answer.51434
  2. Find the area of a triangle with sides 9,11 and 14. Give an exact answer.1217
  3. Find the area of a triangle with sides 9,12 and 13. Give an exact answer.4170
  4. Find the area of a triangle with sides 5,10 and 13. Give an exact answer.614
  5. Find the area of a triangle with sides 6,6 and 9. Give an exact answer.2774
  6. Find the area of a triangle with sides 9,9 and 13. Give an exact answer.131554
  7. Find the area of a triangle with sides 7,7 and 12. Give an exact answer.613
  8. Find the area of a triangle with sides 6,10 and 11. Give an exact answer.4574
  9. Find the area of a triangle with sides 7,9 and 14. Give an exact answer.125
  10. Find the area of a triangle with sides 5,11 and 11. Give an exact answer.15514
  11. Find the area of a triangle with sides 5,14 and 15. Give an exact answer.634
  12. Find the area of a triangle with sides 5,8 and 9. Give an exact answer.611
  13. Find the area of a triangle with sides 3,10 and 11. Give an exact answer.66
  14. Find the area of a triangle with sides 5,6 and 9. Give an exact answer.102
  15. Find the area of a triangle with sides 3,14 and 15. Give an exact answer.426
  16. Find the area of a triangle with sides 4,6 and 6. Give an exact answer.82
  17. Find the area of a triangle with sides 9,11 and 13. Give an exact answer.33354
  18. Find the area of a triangle with sides 4,9 and 11. Give an exact answer.122
  19. Find the area of a triangle with sides 6,14 and 14. Give an exact answer.3187
  20. Find the area of a triangle with sides 8,9 and 13. Give an exact answer.635

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

How to do these

Find the exact area of a triangle with sides 5,6 and 7

  1. s = (5 + 6 + 7) ÷ 2 = 9.
  2. Area = √(9 × 4 × 3 × 2) = √216.
  3. 216 = 36 × 6, so √216 = 6√6.

The answer is 66.

Where students go wrong

Switching to decimals partway through. Writing √216 as 14.7 loses the exact answer the question asks for; factor out the largest perfect square instead.

Also called s formula", or , .

Questions about these worksheets

Yes. Every heron's formula 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.

Precalculus is usually taken around 11th or 12th 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 heron's formula 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.

Using the whole perimeter instead of half of it. s is the semiperimeter, and with the full perimeter every factor is wrong and the area comes out far too big.