TRIANGLE

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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.

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.

A drawing showing a rectangle that has been splitted in
half with the top half dimmed showng a right triangle.

Traditional Formula

Area_Triangle = ½(base x height)

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

NOTES:

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.
HEIGHT is the distance measured at a right angle from the base to the top of the triangle.
This formula works for all triangles.

INTERESTING FACT: The three angles always add to 180°.

Thinking Inside The Box

If you place a RIGHT TRIANGLE inside of a box (a square or a rectangle), you can think of the right triangle as half of the square or rectangle that it is in.

A drawing showing right triangle inside of a rectangle that has been splitted into two triangles with numbers
on top showing the square units.

Another way of showing that the right triangle can be "morphed" into a square or rectangle is to cut it at the middle of the base and "fold" the side that is opposite the right angle back into the triangle to create a square or a rectangle.

A drawing showing a right triangle inside of a box with the midsection of the triangle being cut and triangle folded into the top which create a rectangle.

Yet another way of showing that the right triangle can be "morphed" into a square or rectangle is to cut it at the middle of the height and "fold" the side that is opposite the right angle back into the triangle to create a square or a rectangle.

A drawing showing a right triangle inside of a box with the midsection of the triangle being cut and triangle folded into the bottem which create a rectangle.

KEY: Instead of having to learn another formula (Area_Triangle= ½(base x height)), simply use the rectangle formula in its place and divide the result by 2 to get half of it.

Example

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

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

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

REFERENCE: See screenshots above for graphic representations.

Memorization Tip

To remember the similarities between a triangle and a kite, It is also 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.