MHB Calculate volume of non parallel wedge

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To calculate the volume of a non-parallel wedge, first determine the areas of the triangular bases. The left triangle has an area of 0.4 m², while the right triangle has an area of 1.0 m², resulting in an average area of 0.7 m². The volume is then calculated by multiplying this average area by the wedge's length of 6 m, yielding a total volume of 4.2 m³. It is important to note that the top surface of the wedge is not flat, which may affect further calculations or applications. Understanding these calculations is essential for accurate volume determination in non-standard shapes.
jasonmcbride
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Hi, just wondering how I would calculate the volume of this wedge? see photo attached

IMG_6851.jpg
 
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We have a triangle on the left side with area $\frac 12\cdot 4\,\text{m}\cdot 200\,\text{mm} = 0.4\,\text{m}^2$.
And we have a triangle on the right side with area $\frac 12\cdot 4\,\text{m}\cdot 500\,\text{mm} = 1.0\,\text{m}^2$.
The average triangular area is $\frac{0.4+1.0}{2} = 0.7\,\text{m}^2$.
Multiply by the length to find the volume $V=6\,\text{m}\cdot 0.7\,\text{m}^2=4.2\,\text{m}^3$.

Btw, the top surface is not flat.
 
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Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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