
the same rule applies to non-right triangles
Using a ruler, draw some non-right triangles. Use a horizontal or vertical
grid line for one side (not two) of each triangle.
Draw a bounding rectangle around each triangle. How does the triangle
area relate to the rectangle area?
This shaded area
and this unshaded
area are equal.
It’s easiest to see the relationship if you split
the triangle into two right triangles.
So area of shaded part Sa = Area of unshaded part Ua
So area of shaded part Sb = Area of unshaded part Ub
Shaded part Sa & unshaded part Ua are congruent
Shaded part Sb & unshaded part Ub are congruent
Total shaded area = Sa + Sb = Ua + Ub
So—even for non-right triangles:
You probably didn’t write this
up like this—what matters is
what you got as the answer.
This shaded area
and this unshaded
area are equal.
Sa
Ua
Sb
Ub
U and S just
stand for
Unshaded and
Shaded.
This is the key thing. If you
thought this—even if you
didn’t write it down—then
you’re golden.
Geometry Detective
Solution
162 Chapter 4
AREA = 1/2 THE AREA OF THE BOUNDING RECTANGLE.