Worksheets · Algebra 2

Heron's formula worksheet

Heron's formula needs only the three sides. Work out the semiperimeter s, half of the perimeter, then the area is the square root of s(s - a)(s - b)(s - c). No height and no angle.

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Pick more than one for a sheet that mixes them.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Heron's Formula

Date Period

Find the area of each triangle.

  1. Find the area of a triangle with sides 24,34 and 50
  2. Find the area of a triangle with sides 3,25 and 26
  3. Find the area of a triangle with sides 20,21 and 29
  4. Find the area of a triangle with sides 39,42 and 45
  5. Find the area of a triangle with sides 39,41 and 50
  6. Find the area of a triangle with sides 15,34 and 35
  7. Find the area of a triangle with sides 24,32 and 40
  8. Find the area of a triangle with sides 25,34 and 39
  9. Find the area of a triangle with sides 17,40 and 41
  10. Find the area of a triangle with sides 40,40 and 48
  11. Find the area of a triangle with sides 18,24 and 30
  12. Find the area of a triangle with sides 19,20 and 37
  13. Find the area of a triangle with sides 12,35 and 37
  14. Find the area of a triangle with sides 17,28 and 39
  15. Find the area of a triangle with sides 15,26 and 37
  16. Find the area of a triangle with sides 12,39 and 45
  17. Find the area of a triangle with sides 8,29 and 35
  18. Find the area of a triangle with sides 26,28 and 30
  19. Find the area of a triangle with sides 13,37 and 40
  20. Find the area of a triangle with sides 6,25 and 29

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

Sigma Prep · sigmaprep.io/worksheets

Name

Heron's FormulaAnswer keyVersion 1

Date Period

Find the area of each triangle.

  1. Find the area of a triangle with sides 24,34 and 50360
  2. Find the area of a triangle with sides 3,25 and 2636
  3. Find the area of a triangle with sides 20,21 and 29210
  4. Find the area of a triangle with sides 39,42 and 45756
  5. Find the area of a triangle with sides 39,41 and 50780
  6. Find the area of a triangle with sides 15,34 and 35252
  7. Find the area of a triangle with sides 24,32 and 40384
  8. Find the area of a triangle with sides 25,34 and 39420
  9. Find the area of a triangle with sides 17,40 and 41336
  10. Find the area of a triangle with sides 40,40 and 48768
  11. Find the area of a triangle with sides 18,24 and 30216
  12. Find the area of a triangle with sides 19,20 and 37114
  13. Find the area of a triangle with sides 12,35 and 37210
  14. Find the area of a triangle with sides 17,28 and 39210
  15. Find the area of a triangle with sides 15,26 and 37156
  16. Find the area of a triangle with sides 12,39 and 45216
  17. Find the area of a triangle with sides 8,29 and 3584
  18. Find the area of a triangle with sides 26,28 and 30336
  19. Find the area of a triangle with sides 13,37 and 40240
  20. Find the area of a triangle with sides 6,25 and 2960

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

How to do these

Sides 13,14 and 15

  1. The semiperimeter is 42 / 2 = 21.
  2. Multiply 21 by 8, 7 and 6: that is 7056.
  3. The square root of 7056.

The answer is 84.

Where students go wrong

Using the whole perimeter instead of half of it. s is the semiperimeter, and with the full perimeter the product comes out sixteen times too big.

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.

Algebra 2 is usually taken around 10th or 11th 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 the product comes out sixteen times too big.