Right Regular Prisms and Pyramids

Right Regular Prisms and Pyramids

CAPS Grade 10 works with right regular solids of 3, 4, 5, 6 and 8 sides. "Right" means the axis is perpendicular to the base; "regular" means the base is a regular polygon.

A prism has two identical parallel end faces joined by rectangles. With its axis perpendicular to the HP, the plan shows the true polygon and the elevation is a plain rectangle of the prism's height.

A pyramid has one polygonal base and triangular faces meeting at an apex. With the axis perpendicular to the HP, the plan shows the true base polygon plus lines from each corner to the centre — those are the sloping edges seen from above. The elevation is a triangle.

The critical difference. On a prism, the vertical edges are true length in the elevation. On a pyramid, the sloping edges are not true length in either view — they are inclined to both planes, so their true length must be found by rotation, exactly as in the previous lesson.

Worked example. A square pyramid, 50 mm base, 60 mm high: the elevation's outline slant is not the edge length. The true edge runs from a base corner (not the mid-side) to the apex, and only rotation gives its length.

Core checkpoint: Draw the plan first for a solid standing on the HP. Every point in the elevation projects up from it.