In general the formula to compute such a shape with height $h$, top rectangle $a\times b$ and bottom rectangle $c \times d$, with the $a$ side parallel to the $c$ side, is $\frac16 h(2ab 2cd ad bc)$. Assuming the faces are still plane, the cross-section at height $x$ (measured in $m$) is given by $(10-x)\times(8-\frac 32 x)$, and the volume can be determined by integration to yield $V = \int_0^2(10-x)(8-\frac 32 x)dx = 118 m^3$. If the top and bottom faces of the stack are laid out as hinted in the question, with the bottom $10m$ parallel to the top $8m$ and the bottom $8m$ parallel to the top $5m$, it is neither a trapezium prism nor a truncated pyramid, because the non-horizontal edges do not intersect in a single point. ![]() In case the $8m$ on top and bottom are parallel, you have a trapezium prism, with trapezium area $(10m 5m)/2 \times 2m$ and "height" $8m$ (perpendicular to the trapezium), resulting in a volume of $120 m^3$. Furthermore the question might be ambiguous whether the $8m$ edge of the top face is parallel or perpendicular to the $8m$ edge of the bottom face, and this affects the final result. The pyramid-based answers do not work because the trapezoidal prism is not actually part of a pyramid: the non-horizontal edges do not meet in a single point. Identify the parallel sides of the base (trapezoid) to be $b_ I am confused what is the correct approach. I saw online different methods giving different answers to this question. I also assume a prism is the same thing as a pyramid for geometrical purposes.Ī trapezoidal prism is a 3D figure made up of two trapezoids that is joined by four rectangles. I only confusion I have about this problem is the calculation of the volume of the stack which I believe is the trapezoidal prism (or truncated (right) rectangular prism or frustum of (right) rectangular prism). I know the approach needed to solve this problem. By how many centimetres can the level be raised? ![]() For a plot of land of 100 m × 80 m, the level is to be raised by spreading the earth from a stack of a rectangular base 10 m × 8 m with vertical section being a trapezium of height 2 m.
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