How this calculator works
A right rectangular pyramid has a rectangular base with the apex above its centre. Its four triangular faces come in two matching pairs because the base has two different side lengths. Each pair has its own slant height, found from the pyramid height and half of the opposite base side. The lateral area is the sum of the four triangles, and the volume is one third of the base area times the vertical height.
Formula
V = lwh/3; base area = lw; slant height on length faces = √(h² + (w/2)²); slant height on width faces = √(h² + (l/2)²); lateral area = l × slantLength + w × slantWidth; total area = base area + lateral area.
Worked example
A pyramid with a 6 m by 4 m base and a 5 m height has a volume of 40 m³ and a base area of 24 m². The two slant heights are √29 ≈ 5.385 m and √34 ≈ 5.831 m, giving a lateral area of about 55.635 m² and a total surface area of about 79.635 m².
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Frequently asked questions
Why are there two slant heights?
Each sloping face is a triangle standing on one base edge. The face on a long edge is shorter from rim to apex than the face on a short edge, so the two pairs have different slant heights.
How is this different from a square pyramid?
A square pyramid has equal base length and width, so all four triangular faces match and there is only one slant height. A rectangular base splits the faces into two pairs.
Does the apex have to be centred?
This calculator uses a right pyramid, where the apex sits directly above the centre of the base. An oblique pyramid has the same volume for the same height and base but different slant heights and lateral area.