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i
te this
up like this—wha
t ma
tter
s is
what y
i
te i
t down—then
you’r
e golden.
the same rule applies to non-right triangles
Geometry Detective
Solution
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?
It’s easiest to see the relationship if you split
the triangle into two right triangles.
You probabl
y didn’t wr
T
his s
ea
and this uns
area ar
e equa
l.
T
his s
ea
and this uns
area ar
e equa
l.
Sa
Ua
Sb
Ub
U and S jus
t
s
tand f
or
Uns
So area of shaded part Sa = Area of unshaded part Ua
So area of shaded part Sb = Area of unshaded part Ub
Total shaded area = Sa + Sb = Ua + Ub
So—even for non-right triangles:
AREA = 1/2 THE AREA OF THE BOUNDING RECTANGLE.
T
his is the key thing. If y
ou
thought this—ev
en if y
ou
didn’t wr
162 Chapter 4

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