Head First 2D Geometry

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.