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OBTUSE TRIANGLE

Definition

An obtuse triangle is a 2D shape that has ONE ANGLE MORE THAN 90°.

A drawing showing an obtuse triangle
that has one angle more than ninety degrees.

It Is Helpful To Think

It is helpful to think of an OBTUSE TRIANGLE as a RIGHT TRIANGLE whose right angle has been changed to be MORE THAN 90°.

A drawing showing an right triangle that has been slanted to the left so that then angle is more than ninety degrees.

Traditional Formula

Area_Triangle = ½(base x height)

A drawing showing an obtuse triangle with the measurements for the base and height showing with arrows. The height measurement is taken OUTSIDE the triangle.

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 measured OUTSIDE of triangle at a right angle from the base to the highest point on the triangle.
This formula works for all triangles.

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

Thinking Inside The Box

If you place an OBTUSE TRIANGLE inside of a box (a square or a rectangle), you can think of the obtuse triangle as a "slanted" right triangle which can be thought of as a half of a square or rectangle. (See right triangle section for details)

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

An obtuse triangle with a base of 5 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 5 in)/2 = 20 in/2 = 10 in²

REFERENCE: See screenshots above for graphic representations.

Memorization Tips

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.
Like a parallelogram is thought of as SQUARE or RECTANGLE that has been "pushed from the top, it is helpful to think of an obtuse triangle as a right triangle that has been "pushed" from the BOTTOM.