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Heron's Formula

Use the lengths of the three sides of a triangle to calculate the area.
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This is level 2: calculations for which a calculator is required. You will be awarded a trophy if you get at least 5 answers correct and you do this activity online.

Give all answers correct to three significant figures.

1

Calculate the area of a triangle that has sides with lengths:

13cm, 15cm and 20cm.

☐ \(cm^2\) ☐ ✓ ✗

2

Calculate the area of a triangle that has sides with lengths:

4cm, 14cm and 13cm.

☐ \(cm^2\) ☐ ✓ ✗

3

Calculate the area of a triangle that has sides with lengths:

19cm, 14cm and 15cm.

☐ \(cm^2\) ☐ ✓ ✗

4

Calculate the area of a triangle that has sides with lengths:

14cm, 7cm and 16cm.

☐ \(cm^2\) ☐ ✓ ✗

5

Calculate the area of a triangle that has sides with lengths:

15cm, 20cm and 7cm.

☐ \(cm^2\) ☐ ✓ ✗

6

Calculate the area of a triangle that has sides with lengths:

6cm, 17cm and 18cm.

☐ \(cm^2\) ☐ ✓ ✗

Check

This is Heron's Formula level 2. You can also try:
Level 1 Level 3

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.
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Description of Levels

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Level 1 - Calculations involving whole numbers which can be done without a calculator

Level 2 - Calculations for which a calculator is required

Level 3 - Mixed problems

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Calculating Triangle Area Using Heron's Formula

Given a triangle with sides \(a\), \(b\), and \(c\), follow these two steps to calculate its area:

Step 1: Calculate the Semi-Perimeter

Calculate the semi-perimeter \(s\) using the formula:

$$s = \frac{a + b + c}{2}$$

Where \(s\) is half the perimeter of the triangle.

Step 2: Apply Heron's Formula

Use Heron's Formula to calculate the area \(A\) of the triangle:

$$A = \sqrt{s(s-a)(s-b)(s-c)}$$

Where \(A\) is the area of the triangle.

By following these two steps, you can calculate the area of any triangle when you know the lengths of its three sides.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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