Area of Right Triangles
This lesson presents the idea that the area of any right triangle is exactly half of a certain rectangle, and contains varied exercises for students. To find the area of any right triangle, you simply multiply the lengths of the two sides that are perpendicular to each other, and then take half of that.







1. Find the area of these right triangles. To help you, trace the “helping rectangle” for the triangles.
a. ________ square units b. ________ square units c. ________ square units d. ________ square units e. ________ square units f. ________ square units g. ________ square units h. ________ square units 

To find the area of a right triangle, multiply the lengths of
the two sides that are perpendicular This works because the area of a right triangle is exactly ___________ of the area of the rectangle. 
2. Draw a right triangle whose two perpendicular sides are given below, and then find its area.
a. 1.2 cm and 5 cm
b. 2 1/2 inches and 1 1/4 inches
We can find the area of this houseshape in three parts. 1. The square has an area of 4 × 4 = 16 square units.
2. Triangle 2 has perpendicular sides of 3 and 2 units,
3. Triangle 3 is the same shape and size as triangle 2, Lastly, add the areas: 16 + 3 + 3 = 22 square units in total. 
3. Find the areas of these compound shapes.
a.

b.

c. 
4. Draw a right triangle whose area is 13 square centimeters.
Can you only draw one right triangle with that area, or several different kinds?
Explain.
5. In the grid, draw 3 different right triangles that each have an area of 6 square units.
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.