Know Your Keywords — Math, Advanced
Point 12 — Prisms and pyramids
What do we see?
Prisms and pyramids.
What do we understand?
Break the figure into simpler figures.
Prisms: Volume = base area × h; curved SA (K) = base perimeter × h; whole surface area = 2 × base area + K.
Pyramids: Volume = × base area × h; curved SA (K) = × base perimeter × slant height; whole surface area = base area + K.
Tips & traps
Always ask whether the figure can be distributed into known shapes — a rectangular pyramid is a rectangular base plus 4 triangles.
Question 1 of 3
A square-based pyramid has a surface area of 25000 cm2 and the surface area of just the triangular faces is 15000 cm2. Find the height of the pyramid.