To begin this lesson, click the ‘Create a random triangle’ button below; then, repeatedly click the other button.
Do it again and again and again—make sure you understand what is meant by base/height pairs in a triangle.
(The triangles are randomlygenerated, so you might see some ‘unsatisfying’ situations, like really skinny triangles!)
A precise discussion of base/height pairs follows this JSXGraph exploration.
Take a vertex of a triangle,
and drop a segment that is perpendicular to the opposite side
(first picture below)
or (if needed) to an extension of the opposite side (second picture below).
The segment just created is called a height
or altitude of the triangle,
and the side opposite this vertex is called the corresponding
base.
Since every triangle has three vertices,
every triangle has three
base/height pairs.
If someone asks you for a ‘height and base of a triangle’ there are three possible correct answers!
(Depending on the shape and orientation of the triangle, however, one of these base/height pairs might be most obvious.)
The phrase ‘height (or base) of a triangle’ can refer to the actual line segment,
or to the length of the line segment—the context
will determine which is desired.
Look at the picture at right, where the altitude (from top to bottom)
Convince yourself that the yellow triangles are congruent, This picture shows that the formula for the area of a triangle is half the height, times the base. (Why? Keep reading!)
Here's how to ‘interpret’ the picture. 

With the formula for the area of a triangle in hand,
it is now easy to find area formulas for
quadrilaterals that have at least one pair of parallel sides,
like parallelograms and trapezoids.
Whenever a
quadrilateral has a pair of parallel sides,
then the (perpendicular) distance between these
parallel sides is called the height or altitude,
and the parallel sides are called the bases.
Since a parallelogram has two pairs of parallel sides,
it has two base/height pairs:
The secret to finding the area of a parallelogram is to put in a diagonal,
and observe that
the area is broken into two triangles!
On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. 
PROBLEM TYPES:
