Worksheets · Geometry

Heron's formula worksheet for Geometry

In Geometry Heron's formula is a second route to a triangle's area when no height is given. On an isosceles triangle you can check the result the familiar way: draw the altitude to the base, find it with the Pythagorean theorem, and use one half base times height.

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

Heron's Formula

Date Period

Use Heron's formula.

  1. Find the area of a triangle with sides 51,75 and 78
  2. Find the area of a triangle with sides 13,68 and 75
  3. Find the area of a triangle with sides 42,56 and 70
  4. Find the area of a triangle with sides 35,75 and 100
  5. Find the area of a triangle with sides 21,61 and 68
  6. Find the area of a triangle with sides 26,85 and 85
  7. Find the area of a triangle with sides 39,80 and 89
  8. Find the area of a triangle with sides 37,91 and 96
  9. Find the area of a triangle with sides 24,78 and 90
  10. Find the area of a triangle with sides 29,65 and 68
  11. Find the area of a triangle with sides 33,58 and 85
  12. Find the area of a triangle with sides 30,74 and 88
  13. Find the area of a triangle with sides 13,84 and 85
  14. Find the area of a triangle with sides 36,40 and 68
  15. Find the area of a triangle with sides 51,91 and 100
  16. Find the area of a triangle with sides 70,91 and 91
  17. Find the area of a triangle with sides 51,53 and 100
  18. Find the area of a triangle with sides 24,70 and 74
  19. Find the area of a triangle with sides 34,80 and 82
  20. Find the area of a triangle with sides 43,61 and 68

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

Sigma Prep · sigmaprep.io/worksheets

Name

Heron's FormulaAnswer keyVersion 3

Date Period

Use Heron's formula.

  1. Find the area of a triangle with sides 51,75 and 781836
  2. Find the area of a triangle with sides 13,68 and 75390
  3. Find the area of a triangle with sides 42,56 and 701176
  4. Find the area of a triangle with sides 35,75 and 1001050
  5. Find the area of a triangle with sides 21,61 and 68630
  6. Find the area of a triangle with sides 26,85 and 851092
  7. Find the area of a triangle with sides 39,80 and 891560
  8. Find the area of a triangle with sides 37,91 and 961680
  9. Find the area of a triangle with sides 24,78 and 90864
  10. Find the area of a triangle with sides 29,65 and 68936
  11. Find the area of a triangle with sides 33,58 and 85660
  12. Find the area of a triangle with sides 30,74 and 881056
  13. Find the area of a triangle with sides 13,84 and 85546
  14. Find the area of a triangle with sides 36,40 and 68576
  15. Find the area of a triangle with sides 51,91 and 1002310
  16. Find the area of a triangle with sides 70,91 and 912940
  17. Find the area of a triangle with sides 51,53 and 100714
  18. Find the area of a triangle with sides 24,70 and 74840
  19. Find the area of a triangle with sides 34,80 and 821344
  20. Find the area of a triangle with sides 43,61 and 681290

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

How to do these

Find the area of a triangle with sides 10,10 and 12

  1. s = 32 ÷ 2 = 16, so the area is √(16 × 6 × 6 × 4) = √2304 = 48.
  2. Check: the altitude to the base 12 is √(10² - 6²) = 8, and ½ × 12 × 8 = 48.

The answer is 48.

Where students go wrong

Dropping a factor when two sides are equal. For sides 10, 10 and 12 the product is 16 × 6 × 6 × 4; writing s - 10 only once leaves out a factor of 6.

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.

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 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.