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Head First 2D Geometry by Dawn Griffiths, Stray

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i
te this
up like this—wha
t ma
tter
s is
what y
ou got as the answer.
Shaded.
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
haded ar
ea
and this uns
haded
area ar
e equa
l.
T
his s
haded ar
ea
and this uns
haded
area ar
e equa
l.
Sa
Ua
Sb
Ub
U and S jus
t
s
tand f
or
Uns
haded and
Shaded part Sa & unshaded part Ua are congruent
So area of shaded part Sa = Area of unshaded part Ua
Shaded part Sb & unshaded part Ub are congruent
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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