#### • Class 11 Physics Demo

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# find the area of an unusual shape

Question:

Question:If you have a regular Dodecahedron, which is a platonic solid with 12 pentagons all put together, almost a soccer ball looking, and you want to find the SURFACE area, could you use the formula for the area of a pentagon ( since it's a two dimensional figure) and multiply it by twelve to get the surface area?

Answers:Hi, Yes, that method would work for surface area. I hope that helps!! :-)

Question:my math teacher is making us make this dumbass robot out of geometric shapes and these shapes are 3D. she wants us to find the perimeter and surface area for a all these 3D shapes but wouldn't that just be the surface area?

Answers:You'd want the total length of the all edges, I guess. E.g.: With a cube 1 ft x 1 ft x 1 ft, the edges would add up to 12 ft. Hope you're not using spheres. :) - - - - - - - - - - - - - - - - - - - - - - - - - -

Question:Find any geometric shape that has the same number for its area and perimeter. That is, other than a square (which the only one that works is 4x4), equilateral triangle (only one that works is 4 root 3), and circle (only one that works is radius=2).

Answers:We could try a regular hexagon (regular meaning all interior angles are equal and all edges are equal). According to Wikipedia: A = [3 (3)/2] t And we can easily find the perimeter: P = 6t Equate the two equations: [3 (3)/2] t = 6t Subtract 6t from both sides: [3 (3)/2] t - 6t = 0 Factor out t: t [[3 (3)/2]t - 6] = 0 So [3 (3)/2]t - 6 = 0 [3 (3)/2]t = 6 t = 12/(3 (3)) t = 4/ (3) Thus, a regular hexagon with edge length 4/ (3) has a perimeter equal to its area.