# 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

### Area of Triangles

More Area Worksheets

Perimeter Worksheets

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