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
On this webpage you will find our range of worksheets to help your child to work out the area of a range of right triangles and triangles with their perpendicular height given.
These sheets are graded from easiest to hardest, and each sheet comes complete with answers.
Using these sheets will help your child to:
- know how to find the area of a range of different right triangles;
- know how to find the area of a triangle where the base and perpendicular height are given.
Want to test yourself to see how well you have understood this skill?.
- Try our NEW quick quiz at the bottom of this page.
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What is Area?
- Area is the amount of space that is inside a shape.
- Because it is an amount of space, it has to be measured in squares.
- If the shape is measured in cm, then the area would be measured in square cm or cm2
- If the shape is measured in inches, then the area would be measured in square inches or in2
How To Find the Area of a Right Triangle
- To find the area of a any triangle, you simply need to multiply the base of the triangle by the perpendicular height and halve the answer.
- Because a right triangle has two perpendicular sides already, you simply need to multiply the two perpendicular sides together and halve the result.
- Area of a triangle =½ x b x h, where b is the length of the base and h is the perpendicular height of the triangle.
Area of a Right Triangle Explained
The reason that you simply need to multiply the two perpendicular sides together and halve the answer to find the area of a right triangle is quite straightforward to understand.
If you look at the triangle above, you will notice that the red dotted line that joins the triangle forms a rectangle.
The area of the right triangle is exactly half of this rectangle because it has been split into two identical (congruent) right triangles with the same area.
However, we can also see that the area of the rectangle has to be b x h (because to find the area of a rectangle, you multiply adjacent sides together).
The area of the right triangle is half of this rectangle so we have Area = ½ x b x h.
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
Area of 2D Shapes Printable Support Page
Our printable support page has the formulas for the area of common 2d shapes.
Area of Right Triangles Worksheets
Area of Right Triangles
In Sheets 1 and 2, the perpendicular heights are all given - so they are straightforward to solve.
Sheet 3 is much trickier as Pythagoras' theorem is needed to find the missing perpendicular height before the area can be worked out.
Area of Triangles
These sheets contain a mixture of right triangles and triangles where the perpendicular height is given.
More Recommended Math Worksheets
Take a look at some more of our worksheets similar to these.
5th Grade Geometry Worksheets
Here is our selection of 5th grade Geometry worksheets about angles.
The focus on these sheets is angles on a straight line, angles around a point and angles in a triangle.
More Area Worksheets
Here is our selection of free printable area worksheets for 3rd and 4th grade.
The sheets are all graded in order from easiest to hardest.
Using these sheets will help your child to:
- work out the areas of a range of rectangles;
- find the area of rectilinear shapes.
Perimeter Worksheets
Here is our selection of free printable perimeter worksheets for 3rd and 4th grade.
The sheets are all graded in order from easiest to hardest.
Using these sheets will help your child to:
- work out the perimeter of a range of rectangles;
- find the perimeter of rectilinear shapes.
All the math practice worksheets in this section support Elementary Math Benchmarks.
Volume Worksheets
Here is our range of volume worksheets.
Using these sheets will help your child to:
- know what volume is and how to find it;
- find the volume of shapes by counting cubes;
- find the volume of rectangular prisms;
- solving basic problems involving volume
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.
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We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.
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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