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RIGHT TRIANGLE

DEFINITION

A right triangle is a 2D shape that has ONE RIGHT ANGLE (90°).

A drawing showing a right triangle with one right angle.

SILLY JOKE: Why is the right triangle or right angle not called left triangle or left angle? Because they want to be RIGHT and not WRONG so they want be LEFT behind.

IT IS HELPFUL TO THINK...

It is helpful to think of a RIGHT TRIANGLE as a RECTANGLE or SQUARE that has been cut in half from one corner to another opposite corner.

TRADITIONAL FORMULA

AreaTriangle = ½(base x height) OR base x height/2

A drawing showing showing a right triangle with its height and base measurements with arrows.

DEFINITIONS:

  • The BASE is normally the distance along the bottom of the triangle. However, the base can be any side as long as the height is measured at right angles to the base.
  • The HEIGHT is the distance measured at a right angle from the base to the top of the triangle.

INTERESTING FACT:

  • The three angles always add up to 180°.
  • The above formula works for ALL triangles.

THINKING INSIDE THE BOX METHOD

If you place a RIGHT TRIANGLE inside of a box (a square or a rectangle) and then,

  1. CUT it at the MIDDLE of the base VERTICALLY to create a small right triangle
  2. FOLD the newly created triangle into the original triangle to create a square or a rectangle that is HALF the box it is in

If you place a RIGHT TRIANGLE inside of a box (a square or a rectangle),

  1. CUT it at the MIDDLE of the height HORIZONTALLY to create a small right triangle
  2. FOLD the newly created triangle into the original triangle to create a square or a rectangle that it is in.

KEY: Since a right triangle can be thought of as HALF of a rectangle or square when placed in a box, instead of having to learn another formula (AreaTriangle= ½(base x height)), treat the base as the width and use the rectangular formula (height x width) instead and then DIVIDE THE RESULT BY TWO to get its area. See STEP-BY-STEP SOLUTION for detail example.

STEP-BY-STEP SOLUTION

A right triangle with a base of 6 in and a height of 4 in has an area of:

  1. Treat the base as the width.
  2. Use the rectangle formula instead (AreaTriangle= height x width).
  3. Divide the result by 2.

AreaTriangle = (4 in x 6 in)/2 24 in/2 = 12 in2

MEMORIZATION TIP

Remember, it is helpful to think of a TRIANGLE as HALF of a rectangle or square and a KITE as HALF of a rectangle. Hence, you divide the result by two.