Heron's Formula Worksheets
Free printable heron's formula worksheets with answer keys. Find the area of a triangle from its three sides using Heron's formula: s = (a + b + c) ÷ 2 and…
Using this page
Find the area of a triangle from its three sides using Heron's formula: s = (a + b + c) ÷ 2 and area = √(s(s − a)(s − b)(s − c)). Every triangle on these sheets has a whole-number area, so the working stays clean. Choose between the semi-perimeter only or the full area. Heron's formula is taught in Class 9 in India.
Tips
- Show the working, even when the answer seems obvious; it makes mistakes easy to spot.
- Check each answer: put it back into an equation, or estimate before working out.
- Start with the easier setting and move up once most answers are right.
- Mix one older sheet into each week so earlier skills stay fresh.
Worked example
Sides 13 cm, 14 cm and 15 cm. s = (13 + 14 + 15) ÷ 2 = 21. Area = √(21 × 8 × 7 × 6) = √7056 = 84 cm².
Common mistakes
Using the perimeter instead of the semi-perimeter s.
Forgetting the square root at the end, or leaving out the unit squared.
How to use this generator
Choose the options above the sheet: the number of questions and the settings for this kind of worksheet. Every change makes a new sheet straight away, and New worksheet gives a different set of questions with the same settings.
Each sheet has a worksheet number printed at the top. Type the same number later, or keep the page link, to print exactly the same questions and answer key again. Leave Answer key page ticked to print the answers on a second page, then press Print. Every printed page carries the makekite logo and web address.
Common questions
Do the sides have to be in order?
No. Heron's formula works with the sides in any order, and the sheets shuffle them.
Can I make the sheet harder?
Yes. Use the options above the sheet: more digits, a harder level, brackets or negative numbers where they are offered.
Can I print the same worksheet again?
Yes. Note the worksheet number printed at the top, or keep the link in your browser's address bar, which ends with that number. Entering it later gives the same questions and answers.
Is it free?
Yes. There is no sign-up, and nothing you choose is sent anywhere: the sheets are made in your browser.