HOME BACK

TRIANGLE

Main Menu > Triangle > Acute Triangle

ACUTE TRIANGLE

DEFINITION

An acute triangle is a 2D shape that has ALL THREE ANGLES LESS THAN 90°.

A drawing showing an acute triangle that has all three angles less than ninety degrees.

IT IS HELPFUL TO THINK...

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

Close

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

A drawing showing an acute triangle with the measurement for the base and the height depicted with arrows.

DEFINITIONS:

  • 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 at a right angle to 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 ACUTE TRIANGLE  inside of a box (a square or a rectangle) and then,

  1. PUSH on one of its side from the OUTSIDE 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

KEY: Since an acute 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 acute 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 TIPS

  • 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.
  • It is helpful to think of an acute triangle as "a cute" (pretty) triangle because you can measure its height from WITHIN the triangle. Unlike the obtuse triangle, you have to measure its height from OUTSIDE the triangle because one of its angles must be greater than 90°.
  • To help you remember the shape of an Acute triangle, notice that the side of the capital "A" in Acute goes in the same direction as an Acute triangle.