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Right trapezoidal prism7/24/2023 I'm not sure whether you are expected to know this though. (a) Leo is asked to purchase roping that will be used to close off the area around the statue. As Leo paints the stand, he calculates the surface area of the stand to be 35 ft2. The base of the prism has an area of 3 ft2, and the prism stands 3.2 feet high. Right Prism: A right prism has two flat ends that are perfectly aligned with all the side faces in the shape of rectangles. 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 $\frac16 h(2ab 2cd ad bc)$. The stand is in the shape of a right trapezoidal prism. 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 $V = \int_0^2(10-x)(8-\frac 32 x)dx = 118 m^3$. In contrast, an oblique prism does not have the lateral faces perpendicular to the bases. In simple words, the angle between any lateral face and any base is a right angle. The 2 bases are congruent, aligned perfectly above one another when the prism rests on its base. 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. A right prism is a prism whose lateral faces are perpendicular to its bases. 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. In order to buy enough potting soil to completely fill the window box, he needs to find its volume. By how many centimetres can the level be raised? 20 cm Andrew has a window garden box in the shape of a right trapezoidal prism with dimensions as shown in the figure. ![]() Transcribed image text: (a) Find the surface areas of the figures on the right (a) The surface area of the right trapezoidal prism is cm (Simplify your answer.) 12 cm 2 cm 24 cm 15 cm 15 cm. 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. The Surface area of the trapezoidal Sum of the areas of all the.
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