Understanding Shapes with Oblique Angles

Oblique shapes are extraordinarily common, but many people don’t know what they are. Oblique shapes are shapes made of oblique angles. Oblique angles are:

• Acute angles: angles that are 0-90 degrees
• Obtuse angles: angles that are 90-180 degrees

The sides that form the angles of an oblique shape are never perpendicular. In simple terms, these sides will never meet.

Oblique Shapes

When someone talks about oblique shapes, they refer to a shape, either plane or space, that has either an acute or obtuse (an oblique) angle.

You can figure out if two planes are oblique or not by looking at the angle they create when they intersect. When two plane figures intersect, squares, for example, and create an oblique angle, the planes are called oblique planes.

Oblique Triangles

The most straightforward example of an oblique plane figure to visualize is an oblique triangle. An oblique triangle is any triangle that is not a right triangle. This is because it has an oblique angle and does not contain an angle that is 90 degrees. You can instead call this triangle an acute or obtuse triangle.

An acute triangle has three internal angles of less than 90 degrees. Obtuse triangles have one internal angle greater than 90 degrees; the other two are less than 90. Regardless of the type of triangle, it still follows that all three internal angles will equal 180 degrees.

Finding the Area of Oblique Figures

Finding the area of oblique figures is not that different from finding the area of right figures.

Triangles: base x height / 2 = area

Oblique Space Figures

An oblique space figure, like a rectangular prism, has faces that do not align with the bases. This makes the prism slanted with its base still flush. This is the case for any oblique prism, including a cylinder. The Leaning Tower of Pisa is a fun way to think about oblique space figures. If the figure leans like the tower, it’s oblique.

Note: an oblique space figure is not tipped so that the bottom is balancing on one of its corners. This is simply a tipped right space figure.

Finding the Volume of Oblique Space Figures

Like with plane figures, there really isn’t much of a difference in figuring out the volume of an oblique space figure.

Cylinder: base x height = volume

Pyramid: base x height (of apex when oblique) / ⅓ = volume

Essentially, all formula will remain the same. You must consider any measurement changes that could have happened when the right space figure turned into an oblique prism.

From Parallelogram to Rhombus

There are some shapes out there that we may not use quite often, but they are quite important to know in the realm of oblique planes. One of those figures is a rhomboid. A rhomboid is a parallelogram with oblique, internal angles. When a rhomboid has sides of equal length, it is a Rhombus.

But is a parallelogram oblique? Not always.

If you want to define a parallelogram, it is a quadrilateral with opposite sides equal in length and parallel. Technically, a rectangle can be a parallelogram. When the rectangle is not right, it becomes this oblique shape.

Oblique Pictorials

There is also a type of drawing called an oblique pictorial. You’ve likely drawn the most common oblique pictorial, a cube.

To create an oblique pictorial, you take a plane figure and make it 3D. You do this by extending parallel, angled lines from the figure and connecting the lines to mirror the shape. Usually, these angles are at a 35, 45, or 60-degree angle.

Can you guess why we refer to these drawings as oblique drawings? Look again at the standard angles used to make the plane figure 3D -- they are all less than 90 degrees. Therefore, we draw the extended lines at an oblique angle.

There are three types of oblique pictorial drawings, cabinet, cavalier, and general.

• Cavalier: represents the full depth
• Cabinet: represents half the depth
• General: concerned more with the idea of the pictorial rather than accuracy of depth

Outside of trying to impress your friends in middle school math class with a general oblique pictorial, they have very real-world applications. Eighteenth-century military artists in France used the cavalier pictorial method to design forts. The cabinet projection comes from its application in drawings used in the furniture business.

So when you look at building structures and even your living room furniture, look for the oblique angle that turned its face into a 3D figure.

In Conclusion

Think of what you can call an oblique shape without having to use a protractor to measure the angles -- any imperfect tortilla chip, for one. Identifying oblique shapes is simple once you know what you’re looking for: an acute or obtuse angle! Remember, if it’s not right or a prism is leaning, it’s oblique.

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