Bases and Heights of Triangles

Draw one triangle with an area of 12 square units. Try to draw a non-right triangle.

Explain how you know the area of your triangle is 12 square units.

Constructing the height that corresponds to the given base of an Acute triangle.

(Always remember to click on after every step before moving to the next step.)

  • Clik on ​the Bisector tool .
  • Click on the point A to select it.  ​
  • Click on BC. (A perpendicular line is constructed on BC through A.) ​
  • Click on  and click on the point where the constructed line and BC intersect, G. ​
  • To show that the line is perpendicular to BC, click on   and click on A, G, and B in that order.
  • AG is the height of the triangle for the given base.

Constructing the height that corresponds to the given base of an Obtuse triangle.

  • ​Clik on ​ the line tool .
  • Click on BC to construct a line through both points.​
  • Click on , and click on A. ​
  • Click on BC to construct a perpendicular line to BC.  ​
  • Click on the point tool   and click on the point of intersection of the two lines, D. ​
  • To show that the lines are perpendicular, click on   and click on B, D, and A in that order.
  • AD is the height of the triangle for the given base.

In the three applets below, are copies of the same triangle. Each triangle is rotated so that the side chosen as the base is at the bottom and is horizontal. Draw a height that corresponds to each base.

Draw a line segment to show the height for the chosen base in each triangle.

For each triangle, a base is labeled b. Use the segment tool to draw a line segment that shows its corresponding height.

Select all triangles that have an area of 8 square units.