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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 HELPFULTO THINK...

It is helpful to think of an OBTUSE TRIANGLE as a RIGHT TRIANGLE that has been "SLANTED OUTWARD" so that the right angle is changed to be GREATER THAN 90°.

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

TRADITIONAL FORMULA

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

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 measured OUTSIDE of triangle at a right angle from the base to the highest point on 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 an OBTUSE TRIANGLE  inside of a box (a square or a rectangle) and then,

  1. PUSH on one of its side from the INSIDE to make it a right triangle
  2. CUT it at the MIDDLE of the base VERTICALLY to create a small right triangle
  3. FOLD the newly created triangle into the original triangle to create a square or a rectangle that is HALF the box it is in

IMPORTANT NOTE: If you play the animation above, notice that the size of the box CHANGES to accomodate the size of the obtuse triangle when it is made into a right triangle.


KEY: Since an obtuse 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 DEMO SOLUTION

An obtuse triangle with a base of 4 in and a height of 3 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 = (3 in x 4 in)/2 = 12 in/2 = 6 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.