You will need
10.6 Isometric Drawings
• a ruler
• triangle dot paper
• 3-D models
of 3-D Objects
GOAL
Make realistic drawings of 3-D objects on triangle dot paper.
Learn about the Math
Romona is working on a drawing of the Arc de
Triomphe for a geography project.
can you make a realistic drawing of
? How
a 3-D object?
A. Draw the front face of the Arc de Triomphe so that
the height is vertical and the width is diagonal.
B. Join the bottom right corner to a grid point to show
the depth.
C. Draw a copy of the front face from step A so
that it appears behind the front sketch. Use
the grid point from step B as the back right
corner.
D. Join vertex points on the front face to
matching points on the back face.
E. Erase any lines or arcs that would be
blocked from view by a solid surface.
368 Chapter 10
NEL
Reflecting
1. Why must the back face of the sketch be a copy of the front face?
2. How does joining matching points on the front and back faces make
the sketch look 3-D?
3. How is making an isometric drawing of a 3-D object like making an
isometric drawing of a cube structure? How is it different?
Work with the Math
Example 1: Sketching a realistic diagram
Sketch a realistic diagram of a house, using triangle dot paper and shading.
Paul’s Solution
First I drew the outline of a house.
Then I added details (such as doors and windows) and
used shading to make my diagram more realistic.
Example 2: Using views to make an isometric drawing
Use triangle dot paper and the following top,
front, and right-side views to make a realistic
drawing of the structure.
Bonnie’s Solution
I marked the vertices of
the front and drew the
shape.
NEL
I used the width of the top and
front, and extended the parallel
edges. I finished the back edges.
I shaded parallel faces
to show depth.
3-D Geometry
369
Checking
4. Use triangle dot paper to make an isometric
drawing of this rectangular prism. Look at
a 3-D model if you need help.
6. Make an isometric drawing of each object.
Use triangle dot paper.
a)
b)
Practising
5. Make an isometric drawing of each prism
on triangle dot paper. Look at 3-D models
if you need help.
a)
c)
7. Make an isometric drawing of each object.
a)
b)
b)
370 Chapter 10
NEL
7. c)
Extending
9. Choose an object in a picture in this lesson.
Make an isometric drawing of the object
from a different view.
d)
10. a) Choose an object in the classroom.
Make an isometric drawing of it.
b) Make an isometric drawing of the same
object from a different view.
c) Explain how your drawings in parts (a)
and (b) are the same and how they are
different.
11. a) Make an isometric drawing of a prism
that has a pentagonal base.
b) Explain how you chose the view for
your drawing in part (a).
8. Make an isometric drawing of each view of
the recipe box on triangle dot paper.
a)
12. Explain why an isometric drawing looks 3-D.
13. Make an isometric drawing of the object
whose top, front, and side views are
shown below.
b)
NEL
3-D Geometry
371