Area of Right Triangle

Welcome to our Area of Right Triangle page.

Here you will find our collection of worksheets all about finding the area of a right triangle.

These sheets are aimed at children of a 5th / 6th grade level and up.

Area of Right Triangles

Area of Right Triangle Examples

Example 1) Find the area of the right triangle below.

• In the example above, the base is 8cm and the perpendicular height is 5cm.
• So the area of right triangle is ½ x 8 x 5 = ½ x 40 = 20 square cm or 20 cm2

Example 2) Find the area of the right triangle below.

• In the example, the base is 9m and the perpendicular height is 4m.
• So the area is ½ x 9 x 4 = ½ x 36 = 18 square cm or 18 cm2

Example 3) Find the area of the triangle below.

• In the example, the triangle is not actually a right triangle.
• However, we see that the perpendicular height is 4cm and the base is 6cm.
• The perpendicular line creates two right triangles out of the larger triangle.
• The area of this triangle is exactly half the area of the rectangle formed by the triangle and the red dotted line.
• So the area is ½ x 6 x 4 = ½ x 24 = 12 square cm or 12 cm2

Example 4) HARDER - Find the area of the right triangle below.

• So why is this example much harder?
• It is because we do not know the perpendicular height.
• To find the perpendicular height we can use Pythagoras' theorem becuase it applies to right triangles.
• So if we call the missing side b, then Pythagoras' theorem gives us:
• h2 = a2 + b2, where h is the hypotenuse and a and b are the other two sides.
• So 52 = 42 + b2
• So 25 = 16 + b2
• So b2 = 25 - 16 = 9
• So b = 3cm.
• We can now find the area now we have found the perpendicular side.
• Area = ½ x 4 x 3 = ½ x 12 = 6 square cm or 6 cm2

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

More Area Worksheets

Perimeter Worksheets

Area of a Right Triangle Quiz

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

We do not collect any personal data from our quizzes, except in the 'First Name' and 'Group/Class' fields which are both optional and only used for teachers to identify students within their educational setting.

We also collect the results from the quizzes which we use to help us to develop our resources and give us insight into future resources to create.

This quick quiz tests your skill at finding and using the area of a right triangle with our quick quiz here!

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