Head First 2D Geometry

triangle properties

A triangle fits inside a bounding rectangle

A bounding rectangle is a box that fits tightly

around the triangle.

Not this sort

of bounding

1

To draw a bounding rectangle:

2

3

Pick a side of your triangle to share

with the bounding rectangle.

Draw a line parallel to this side,

touching the opposite vertex.

Draw two perpendicular lines,

one at each of the other

vertices.

How does the shaded area of triangular field A compare with

the area of the dashed bounding rectangle surrounding it?

Scale: 1cm = 30m

60m

90m

Field A

you are here 4 157

They share

this side.

This box is

the bounding

rectangle.

Here’s the top

(opposite) vertex.

triangle area is half

158 Chapter 4

Both methods give you the

same answer: half.

How does the shaded area of triangular field A compare with

the area of the dashed bounding rectangle surrounding it?

Scale: 1cm = 30m

60m

90m

Field A

There are two different ways to think about this question....

1.

There’s a shaded triangle representing the

part of the rectangle which is the field.

And there’s an unshaded triangle representing the

part of the rectangle which isn’t the field.

Field A

Not

field A

90m

60m

109m

90m

60m

109m

If the triangles are congruent, then they must

both have the same area, so they share the

rectangle area equally—half each.

2. You might have recognized visuall ...