How to Draw a Three Dimensional Rectangle?

Have you ever wondered what the commonly used term for a three-dimensional rectangle in the world of mathematics is called? Well, it is known as a ‘rectangular-shaped prism’. And technically speaking, a rectangle is a three-dimensional shape and not a form. Though both ‘form’ and ‘shape’ are two essential art elements, the importance lies between one being two dimensional or three dimensional.

To get an answer with more details, you have to dive a bit deeper, while comprehending or learning measurement. Initiate with a two-dimensional rectangle, which is well-defined by four vertex points or corners. The construction of these corners mainly depends upon the Cartesian Coordinate System. For instance,

Top-most left measurement: (x = 0, y = 5)
Top-most right measurement: (x = 10, y = 5)
Bottom-left measurement: (x = 5, y = 0)
Bottom-right measurement: (x = 10, y = 0)

Thus, it has a thickness of 10 and height of 5.

At this point, add a third dimension, giving the rectangle a depth or thickness of 4; adding requirements of four more points

Top-most left front: (x = 0, y = 5, z = 4)
Top-most right front : (x = 10, y = 5, z = 4)
Bottom-left front: (x = 5, y = 0, z = 4)
Bottom-right front: (x = 10, y = 0, z = 4)

You can also re-word the initial 4 points as the ‘back’ of the vertices, by catering to them with Z values of 0:

Top-left back: (x = 0, y = 5, z = 0)
Top-right back: (x = 10, y = 5, z = 0)
Bottom-left back: (x = 5, y = 0, z = 0)
Bottom-right back: (x = 10, y = 0, z = 0)

Finally, all the eight vertices are readily present, providing a three-dimensional rectangular prism of width 10, height 5, and thickness 4. While making a three-dimensional rectangle, there is no requirement for the ‘axis-alignment’ of the object as presented here. Also rotate the same, depending on the question. This is the simplest way to make/ draw, a three-dimensional rectangle mathematically.

With detailed know-how, drawing any three-dimensional object becomes way more impressive, and something a bit more practical to use in your mathematical drawings. We are going to learn how to draw a free-hand three-dimensional rectangle while using the concept of two-point perspectives. Moreover, try not to draw your three-dimensional rectangles by making use of the overlapping square technique.

Let us initiate the journey with our tutorial on ‘how to draw a three-dimensional rectangle’, in the most user-friendly manner.

Lesson objectives

The perfect amalgamation of Math and Art gets students to think about the various shapes and objects from multiple perspectives. Different questions might keep coming your way, like

Can a student construct something innovative from their three-dimensional rectangular designs?
When and where can they proceed with the same?
Will students just get the knowledge of the basic techniques?

Worry not, as the step-by-step guide will help prepare a student for sketching and graphically rendering three-dimensional rectangles in their future lessons.

Required drawing materials

Technical, drawing, or regular pens and pencils
Protractors
Eraser
Measuring scale or rulers
A sheet of paper/ isometric paper
Drawing board

Draw a three-dimensional rectangle – A six step guide

For ‘perspective drawings’ one has to find the vanishing point and draw rays extending from that particular point. Many struggle when drawing a three-dimensional rectangle, while getting the know-how on the concepts involved in the same. At the same time, a handful of students make use of the technical aspects while drawing a three-dimensional rectangle in a ‘picture-perfect’ manner. Keep following the six-step guide for marking the perfect three-dimensional rectangle in perspective, while keeping a note of the required measurements in mind.

Step #1 – Draw the closest corner

With the aid of several ways of drawing the rectangle, you should initiate by viewing the object from your perspective. For instance, if you are considering your rectangular-shaped item, one-point perspective is what you should implement. And for 3/4th perspective, you should implement the concept of two-perspective. Start drawing the three-dimensional rectangle from the corners of the same that is closest to you.

Step #2 – Draw the edges at the bottom

Then, starting from the edges at the bottom of the rectangle, simultaneously draw two lines in the form of a ‘V’. The overall shape of the rectangle will depend upon the length of the lines. And for an even rectangle, you ought to keep these lines, approximately, of a similar size.

Step #3 – Draw the edges at the top

Following the same, draw the lines for the rectangle’s upper edge facing closet to you, forming a minor ‘V’. These lines should be parallel to the consistent lines on the bottom of the rectangle. Keep a note of the similarity between the top and bottom lines at the left corner, with the right-side ones.

Step #4 – Draw all the sides

While drawing all the sides, you should connect these lines with two vertical lines. And both should run parallel with the initial corner line of your rectangle. Please note that without these three lines being parallel with each other, your rectangle will start looking disoriented.

Step #5 – Draw the furthest edges

Now it is time to draw the edge of the rectangle, which is furthest. Yet again, keep these lines parallelly placed with their counterparts, crosswise from them. Thus, keep the lines that are shorter, facing parallel to each other; at the same time, repeat the same for the long lines.

Step #6 – Add depth to a three-dimensional rectangle

Lastly, you need to add depth to the three-dimensional rectangle; a line parallel to the three other vertical lines. Add on to some thickness or depth to the rectangle with some surplus lines to the same. But, keep these lines parallel. Your three-dimensional rectangle is ready!

Shade the three-dimensional rectangle

Yet another significant aspect related to drawing a three-dimensional rectangle is none other than shading. Before starting with your shading process, try to appreciate the source of light!

Initiate with shading the three-dimensional rectangle from the ‘darkest’ corner.
Eliminate the actual source of light from the upper left-hand corner of the three-dimensional rectangle.
Create a shadowy effect on the opposite side of the three-dimensional rectangle.
Gradually proceed from the darker to the lighter side.
Keep the mid-section of the rectangle until the end.
After shading, add-on a cast shadow on the furthest side of the three-dimensional drawing of the rectangle.
You will find that it is comparatively darker than its sides.

With all the correct mathematical measurements, drawing a perfect three-dimensional rectangle with shading is equally essential. It is not that all have to be 100% accurate. But by getting a piece of knowledge on the basic concepts along with some guided practice, you will enable you to draw the right three-dimensional rectangle.

Drawing vocabularies for a three-dimensional Rectangle

Two-dimensional: An object having only two dimensions, mainly just the length and the width.
Three-dimensional: An object having three dimensions, mainly concerning the height, width along with the length.
Orthographic drawings: Related drawings from multiple view-points; usually from the front, top, and sideways showing a three-dimensional object in two dimensions.
Perspective: A mode of visualising and drawing, which allows the artists to represent three-dimensional scenes in the form of two dimensions.
Shape: It is a two-dimensional element formed from lines, being both negative or positive.
Form: It is the addition of depth to a two-dimensional shape for turning the same into a three-dimensional one.
Value: It is a word for the colours’ lightness or darkness while defining the tones from black to white.
Shadow: It is the dark portion where a solid object blocks the light originating from a source.
Parallel lines: These are two individual lines, always staying apart at the same distance without touching each other.
Light source: It is the origin of light.
Shading: Its effective use stands for specific drawing purposes, mostly to highlight the lighter to darker sides. You can also create the illusion of depth with this.
Cast shadow: An object blocking the light casting a shadow on the ground or another surface.

Final point

‘Practice makes a man perfect!’

Keep this famous saying alive by drawing a three-dimensional rectangle and learning measurements. Go on an artistic spree in mathematics! Keep having fun while practising.

With the right steps under your garb, you now have a fair idea of drawing the ‘picture-perfect’ three-dimensional rectangle. You can put this recently gained knowledge to test with Cuemath’s expert tutors. Get into the right track and know more by availing the trial class for free. With the aid of customised learning plans and individual focus, it assists students in building confidence. So, be the perfectionist and keep learning newfound concepts to draw the finest of the three-dimensional rectangle.