In the assignment Areas of Triangles we saw the formula
We will investigate heights of triangles in this assignment. The line passing through a vertex of a triangle that is perpendicular to the opposite side is called an altitude of the triangle. Each triangle has three altitudes.
Problem 1. On a separate piece of paper, trace each of the triangles above. For each triangle, draw the altitude to each side. Measure, in centimeters, each side and the corresponding altitude, and calculate the area according to the formula for each pair of side and altitude.
Problem 2. Did you get exactly the same number for each of your three calculations of the area of the largest triangle? If you did not, what could explain why you did not get the same value each time?
Look at your triangles with the three altitudes drawn in them. Is there anything that strikes you about the pictures?