G3 · Top, Front and Side Views of 3-D Objects

Alberta Grade 11 Mathematics

Geometry

Read and draw top, front, and side views

What you will learn

• Describe a 3-D object using its length, width, and height.
• Model a simple object with a sketch or unit cubes.
• Draw and label its top, front, and side views.
• Check that the views agree with the object’s dimensions.

Start with the object and its dimensions

• Choose and label the front before making the views.
• The top view shows length and width.
• The front view shows length and height.
• The side view shows width and height.

Make each view match the object

• Draw each view as if looking straight toward the object.
• Views that share a dimension must show the same measurement for it.
• Use visible outlines and edges; do not add details that cannot be seen.

A clear drawing is a useful model

• Label the object and each view.
• Write units with measurements.
• Check matching dimensions across views.

Which dimensions appear in each view?

Worked example

Views of a storage box

1. Identify the object
   The box is a rectangular prism. Its stated measurements are length 60 cm, width 30 cm, and height 40 cm. The long face is the front, so the front view uses the length and height.
2. Match dimensions to views
   Looking down shows the length and width. Looking straight at the front shows length and height. Looking at the right side shows width and height. Each view is therefore a rectangle with the corresponding pair of measurements.
   $$\text{top: }60\text{ cm}\times30\text{ cm};\quad \text{front: }60\text{ cm}\times40\text{ cm};\quad \text{right side: }30\text{ cm}\times40\text{ cm}$$

Worked example

Check a set of proposed views

1. Recall what the side view shows
   The right-side view shows the object's width and height. The height is 20 cm, and the width is 50 cm. Therefore, the 55 cm label cannot describe this box's right-side view.
2. Correct the measurement
   Replace 55 cm with the stated width, 50 cm. Then compare shared dimensions: the top and side views both use width, and the front and side views both use height.
   $$\text{right side: }50\text{ cm}\times20\text{ cm}$$

Worked example

Model a low platform

1. Assign the dimensions
   The platform is a rectangular prism. Its long face is the front, so the front view uses 1.2 m and 0.25 m. No conversion is needed because all measurements use metres.
2. Describe all three views
   The top view uses length and width. The front view uses length and height. The right-side view uses width and height. Each view is rectangular because the platform has straight rectangular faces.
   $$\text{top: }1.2\text{ m}\times0.8\text{ m};\quad \text{front: }1.2\text{ m}\times0.25\text{ m};\quad \text{right side: }0.8\text{ m}\times0.25\text{ m}$$

Common mistakes and how to avoid them

Lesson summary

• A 3-D object can be described by its length, width, and height.
• The top view shows length and width; the front shows length and height; the side shows width and height.
• Choose the front direction, label views, and include units.
• Check that dimensions shared between views agree.

Check your understanding

Key terms

Three-dimensional object

An object with length, width, and height.

Model

A drawing or representation that shows useful information about an object.

Orthographic view

A flat drawing made by looking straight at an object from one direction.

Rectangular prism

A box-shaped solid with rectangular faces.

Unit cube

One equal-sized cube used as a part of a model.

Continue through Math 20-3

View the complete Math 20-3 Alberta Grade 11 Mathematics curriculum and lessons

• G2 · Solve practical scale and scale-diagram problems
• G4 · Draw and describe simple exploded views and scaled components
• G1 · Solve problems involving two or three right triangles
• M2 · Solve volume and capacity problems with SI and imperial units
• N1 · Use and verify strategies for numerical puzzles and games
• N3 · Explain and calculate compound-interest growth

Tutor support for G3 · Model 3-D objects and draw their top, front, and side views

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برای مبحث G3 · اجسام سه‌بعدی را مدل کنید و نماهای بالا، روبه‌رو و کنار را رسم کنید در درس Math 20-3، سؤال و تلاش خود را همراه بیاورید. در جلسه می‌توانید گام‌های تلاش خود را نشان دهید و آن را با یک نمونهٔ حل‌شده مقایسه کنید. راهنمای معلم ریاضی را ببینید یا جلسهٔ معارفهٔ رایگان ۳۰ دقیقه‌ای درخواست کنید. زمان جلسه پس از پذیرش معلم قطعی می‌شود.

About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Alberta Grade 11 Mathematics (Math 20-3), expectation G3. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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