This lesson presents the idea that the area of any triangle is exactly half of a certain parallelogram  thus we get the familiar formula of multiplying the base and the altitude, and taking half of that. The lesson contains varied exercises for students.
Area of Triangles

1. Find the area of the shaded triangle in the picture
above.
2. Draw the corresponding parallelograms for these triangles, and find their
areas.
Hint: draw a line that is congruent to the base of the
triangle, starting at the top vertex.
a. _______ square units 
b. _______ square units 
c. _______ square units 
Again, we use a base and an altitude.
The altitude is perpendicular
to the base,

Since the area of a triangle is half of
the area of



3. Draw an altitude in each triangle, and mark the base. Find the area of each triangle.
a. _______ square units 
b. _______ square units 
c. _______ square units 



5. This figure is called a _________________________.
Calculate its area. 
6. Draw as many differentshaped triangles as you can that have an area of 12 square units.

8. Draw your own triangle, and find its area!
9. Draw a triangle with an area of 3 square inches.
Is it only possible to draw just one triangle with
that area, or is it possible draw several, with
varying shapes/sizes?
10. Draw a triangle,
without measuring anything, so that its area is close to 20 cm^{2}.
Check by drawing
the altitude and measuring! Practice until you get
a triangle with an area of approximately 20 cm^{2}.
You can even make a game
out of this: whoever gets the area the closest to the given area is the
winner
or gets the most points. Or, take turns with your friend, asking the friend to
draw a triangle with
a specific area. Perhaps add a condition that the
triangle has to be obtuse/acute/right, or
equilateral/isosceles/scalene.
This lesson is taken from Maria Miller's book Math Mammoth Geometry 2, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.
Math Mammoth Geometry 2
A selfteaching worktext for 6th7th grade that covers the area of triangles, parallelograms, and polygons, pi, area of circle, nets, surface area, and volume of common solids.
Download ($5.70). Also available as a printed copy.