AREA OF TRIANGLES AND RECTANGLES

A logical extension to our triangle coordinates and classify game was finding the area of triangles.

First, we explored the area of rectangles with horizontal and vertical base and height dimension. Even though some of the younger Mathletes say that they don’t know multiplication can clearly see how finding area is really repeated addition and easy to visualize. Triangles that have the same horizontal base and vertical height as a corresponding rectangle were also easy for the children to visualize as long as the triangle was right or acute. They would just take half of the area of the rectangle.

Visualizing the area of an obtuse triangle with the same base and height as a corresponding rectangle was more challenging. As soon as they could see that the height is always perpendicular (right angle) to the base, it became easier.

The most challenging part of this lesson was finding half of the rectangle's area when and odd number. For example, when looking for the area of a 3x3 right triangle. Half of 9 is the sum of half of 8 plus half of one or 4 plus 1/2 or 4 1/2. 25/2 = 24/2 + 1/2 = 12 1/2.

The older Mathletes (grades 3-5) were challenged to find the area of triangles that do not have horizontal and vertical base and height. Here, they had to first draw auxiliary lines to make right triangles off of each side of the triangle and list the dimensions. Then they found the area of each of these right triangles and add them up. Finally, they would subtract the right triangle sum from the larger rectangle created by forming the additional right triangles. This would give them the original triangle.

This lesson required them to see the auxiliary lines that would make a circumscribed rectangle, multiplication, division, adding and subtraction.

See the pdfs attached and make your own triangles, list the dimensions, and figure out the area of each.