Problem

A large rectangle is in the first quadrant of the Cartesian plane with its four vertices at \((0,0)\), \((8,0)\), \((8,4)\), and \((0,4)\). It is divided into eight regions labelled \(A\), \(B\), \(C\), \(D\), \(E\), \(F\), \(G\), and \(H\), as shown.

Region \(A\) is a \(3\) by \(2\) rectangle with vertices at \((0,0)\), \((3,0)\), \((3,2)\), and \((0,2)\).
Regions \(B\) and \(C\) make up the top \(8\) by \(2\) rectangle with vertices at \((0,2)\), \((8,2)\), \((8,4)\), and \((0,4)\). \(B\) is a right-angled triangle with vertices at \((0,4)\), \((0,2)\), and \((4,2)\). \(C\) is a right trapezoid with vertices at \((0,4)\), \((8,4)\), \((8,2)\), and \((4,2)\).
Regions \(D\), \(E\), \(F\), and \(G\) make up the \(4\) by \(2\) rectangle with vertices at \((4,0)\), \((8,0)\), \((8,2)\), and \((4,2)\). The two diagonals of this rectangle meet at \((6,1)\) dividing it into four triangles. \(E\) and \(D\) are the top and bottom triangles, respectively, and \(F\) and \(G\) are the left and right triangles, respectively.
Region \(H\) is the \(1\) by \(2\) rectangle with vertices at \((3,0)\), \((4,0)\), \((4,2)\), and \((3,2)\).

What fraction of the area of the large rectangle is the area of region \(A\)? the area of region \(B\)? the area of region \(C\)? the area of region \(D\)?

Problem of the Week Problem B Fraction Fun

Problem of the Week
Problem B
Fraction Fun