Oblique Prism

High School

Definition

A prism whose end planes are parallel but not aligned on top of one another perfectly. An oblique prism's lateral faces (its sides) are parallelograms. Since its bases don't align perfectly, the prism looks like it is slanted (oblique means "slanting").

Worked examples

A rectangular prism with base \(4 \times 3\) and height \(5\), but the top face shifted sideways so edges slant.

The bases are parallel rectangles but not directly above each other, making the lateral faces parallelograms.

Volume: \(V = B \cdot h = (4 \times 3) \cdot 5 = 60\) cubic units

Volume formula stays the same as a right prism: base area times perpendicular height.

Common mistakes

Using slant height instead of perpendicular height in \(V = B \cdot h\) → \(h\) is the perpendicular distance between bases, not the slanted edge length The height must be measured straight up, perpendicular to the base, even though the prism leans.
Thinking lateral faces are rectangles → Lateral faces of an oblique prism are parallelograms Because the top base is shifted, the side faces slant and become parallelograms, not rectangles.
Confusing oblique prisms with pyramids → Oblique prisms have two parallel congruent bases; pyramids taper to a point A prism always has two identical bases; slanting does not turn it into a pyramid.

Where you'll use it next

You'll apply oblique prisms when calculating volumes of slanted structures in geometry and solid figures, and later in calculus when using Cavalieri's principle to compare solids with matching cross-sections.

Found in 1 StudyPug lesson

Surface Area and Volume of Prisms: Essential Geometry Concepts

Geometry

Dive into the world of prisms! Learn to calculate surface area and volume, master key formulas, and apply your skills to real-world problems. Boost your geometry prowess with our comprehensive guide.

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