Head First 2D Geometry

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