Right-angled triangles are triangles containing a single 90° angle.
It is called a right angle. The right angle is usually in one of the bottom corners, but it doesn’t have to be.
They come in isosceles and scalene variations.
Right-angled isosceles triangles
These have one right angle and two other equal angles of 45°.
They have two equal sides and one long side. The hypotenuse of a triangle is always its longest side.
Scalene right-angled triangle
These have one right angle but two other unequal angles.
It has no equal sides.
Like all triangles, the three angles on these triangles always add up to 180°.
Finding the area of a right-angled triangle
The area of a right-angled triangle uses the same formula as the area of any triangle. It helps to think of a triangle as half of a quadrilateral (a 2D shape with four sides). A right-angled triangle is the same as half of a square or a rectangle because of the right angle.
The formula for finding the area of a right-angled triangle is 1/2 × base × height.
The bottom line of the triangle is the base, and the line at the side is the height. So if you were finding the area of a rectangle, you would multiply the base by the height. However, because a triangle is half the size of a rectangle, you have to multiply the product of the base and the height by 1/2 to get to half of the answer.
For example, imagine the orange right-angled triangle in the picture above.
If the base was 10 cm and the height was 6 cm, we would multiply those together to get 60 cm².
Then, we would multiply that by 1/2 to get 30 cm². That would be the area of the right-angled triangle.
Don’t forget: when you write the area of a shape, you must put a small “2” above the measurement. For example, cm² or m².
