Polyhedrons

Geometry Level pending

![](https://ds055uzetaobb.cloudfront.net/uploads/RjRYMdFLya- i m g 2 018031 9 1 51541. j p g ) : . c e n t e r img_20180319_151541.jpg){: .center} In the figure, polygon A,E,Fare isosceles right triangles ;B,C D are squares With sides of length1; and G is an equilateral triangle. The figure can be folded along its edges to form a polyhedron having the polygons as faces.The volume of polyhedron is?

4/6 3/2 1/2 5/6

Sangsuddha Mukherjee by Sangsuddha Mukherjee , 17, India

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1 solution

It is clear that the side of the equilateral triangles are √2. The volume is calculated by removing a tetrahedron from the whole figure by placeing one of the three right triangles as the base it has an area of 1/2.The height is the height of one of the two remaining right triangles-the equilateral triangle is slanted not the height. Thus the volume of the tetrahedron is 1/3×1/2×1=1/6 that is the remains volume is 5/6

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