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PAU Madrid 2024-25 · Net of the frustum
Statement. The pyramid has a square base, 4 units side and 6 units height. It is cut by a horizontal plane at mid-height (z = 0). Find the net of the resulting frustum. (Adaptation of the original statement: the exam gives the figure; the measurements are fixed here so it can be built in the editor.)
Step-by-step solution
- The horizontal cut at mid-height leaves a frustum with a square base of 4 units and a square top of 2 units.
- The four lateral faces are isosceles trapezoids. Their height is the apothem of the face: in the complete pyramid it is sqrt(6^2 + 2^2) = 6.32 units, and in the frustum half of that, 3.16 units.
- Unfold the base and, around each side, its trapezoid. In the drawing the top is placed separately, in true size.
- Each trapezoid is built in true size; in the projection the lateral edges are not seen in true length.
- Check the area: base + four trapezoids + top.
Result
Net area = 57.95 u2 (base 16 + sides 37.95 + top 4).