Oblique Pyramid

High School

Definition

A pyramid whose apex is not above the center of the pyramid's base. The pyramid looks as if it is tilted to one side (oblique means "slanting"). In order to calculate a oblique pyramid's surface area, you cannot use the regular formula anymore and must instead cauculate each of the faces seperately.

Worked examples

A square pyramid with base side \(6\) cm and apex directly above one corner (not the center).

The apex is off-center, so the slant heights of the four triangular faces are all different lengths.

To find surface area: calculate base area \(+ \) area of each triangular face separately using \(\frac{1}{2}bh\).

Each triangle has a different height because the pyramid is tilted; measure or calculate each one.

Common mistakes

Using \(\)SA\( = B + \frac{1}{2}P\ell\) for an oblique pyramid → Calculate the area of each face individually and sum them The slant height formula only works for right pyramids where the apex is centered.
Assuming all lateral faces have the same area → Each triangular face has a different slant height and area The off-center apex means each face slants at a different angle.
Confusing oblique with obtuse → Oblique means slanted/tilted, not an angle measure Oblique describes the pyramid's tilt; obtuse describes angles greater than 90°.

Where you'll use it next

You'll use oblique pyramids when studying three-dimensional geometry in later courses, engineering applications, and architectural design where structures are intentionally tilted for aesthetics or stability.

Found in 1 StudyPug lesson

Surface area and volume of pyramids

8th Grade Math

The surface area of a pyramid basically contains four triangles and a rectangle as its base. Therefore, if you know how to find the area of triangles and rectangles, we can calculate the surface area of pyramids quite easily. Also, there is a formula for calculating the volume of pyramid too. We will also look at some composite solid questions in this lesson.

8th Grade8th