Worksheets · Algebra 2

Heron's formula worksheet for Algebra 2

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.

Also taught in Precalculus and Geometry, 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

Heron's Formula

Date Period

Use Heron's formula.

  1. Find the area of a triangle with sides 45,60 and 75
  2. Find the area of a triangle with sides 7,65 and 68
  3. Find the area of a triangle with sides 29,52 and 69
  4. Find the area of a triangle with sides 39,62 and 85
  5. Find the area of a triangle with sides 56,61 and 75
  6. Find the area of a triangle with sides 26,73 and 97
  7. Find the area of a triangle with sides 20,51 and 65
  8. Find the area of a triangle with sides 9,73 and 80
  9. Find the area of a triangle with sides 78,89 and 89
  10. Find the area of a triangle with sides 12,55 and 65
  11. Find the area of a triangle with sides 40,68 and 84
  12. Find the area of a triangle with sides 39,58 and 95
  13. Find the area of a triangle with sides 34,55 and 87
  14. Find the area of a triangle with sides 30,52 and 74
  15. Find the area of a triangle with sides 51,75 and 84
  16. Find the area of a triangle with sides 33,56 and 65
  17. Find the area of a triangle with sides 45,45 and 72
  18. Find the area of a triangle with sides 32,65 and 65
  19. Find the area of a triangle with sides 18,80 and 82
  20. Find the area of a triangle with sides 75,75 and 90

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

Sigma Prep · sigmaprep.io/worksheets

Name

Heron's FormulaAnswer keyVersion 1

Date Period

Use Heron's formula.

  1. Find the area of a triangle with sides 45,60 and 751350
  2. Find the area of a triangle with sides 7,65 and 68210
  3. Find the area of a triangle with sides 29,52 and 69690
  4. Find the area of a triangle with sides 39,62 and 851116
  5. Find the area of a triangle with sides 56,61 and 751680
  6. Find the area of a triangle with sides 26,73 and 97420
  7. Find the area of a triangle with sides 20,51 and 65408
  8. Find the area of a triangle with sides 9,73 and 80216
  9. Find the area of a triangle with sides 78,89 and 893120
  10. Find the area of a triangle with sides 12,55 and 65198
  11. Find the area of a triangle with sides 40,68 and 841344
  12. Find the area of a triangle with sides 39,58 and 95456
  13. Find the area of a triangle with sides 34,55 and 87396
  14. Find the area of a triangle with sides 30,52 and 74624
  15. Find the area of a triangle with sides 51,75 and 841890
  16. Find the area of a triangle with sides 33,56 and 65924
  17. Find the area of a triangle with sides 45,45 and 72972
  18. Find the area of a triangle with sides 32,65 and 651008
  19. Find the area of a triangle with sides 18,80 and 82720
  20. Find the area of a triangle with sides 75,75 and 902700

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 every factor is wrong and the area comes out far 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 every factor is wrong and the area comes out far too big.