Volume of Prism Given Net (2022 AMC 8 P24)
Source:
January 25, 2022
geometryrectangle3D geometryprismAMC 82022 AMC 8
Problem Statement
The figure below shows a polygon , consisting of rectangles and right triangles. When cut out and folded on the dotted lines, the polygon forms a triangular prism. Suppose that and . What is the volume of the prism?[asy]
// djmathman diagram
unitsize(1cm);
defaultpen(linewidth(0.7)+fontsize(11));
real r = 2, s = 2.5, theta = 14;
pair G = (0,0), F = (r,0), C = (r,s), B = (0,s), M = (C+F)/2, I = M + s/2 * dir(-theta);
pair N = (B+G)/2, J = N + s/2 * dir(180+theta);
pair E = F + r * dir(- 45 - theta/2), D = I+E-F;
pair H = J + r * dir(135 + theta/2), A = B+H-J;
draw(A--B--C--I--D--E--F--G--J--H--cycle^^rightanglemark(F,I,C)^^rightanglemark(G,J,B));
draw(J--B--G^^C--F--I,linetype ("4 4"));
dot("",A,N);
dot("",B,1.2*N);
dot("",C,N);
dot("",D,dir(0));
dot("",E,S);
dot("",F,1.5*S);
dot("",G,S);
dot("",H,W);
dot("",I,NE);
dot("",J,1.5*S);
[/asy]