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The figure below represents a window, with the shaded regions representing the openings for the glass. If all line segments in the figure are either horizontal or vertical and the openings are all the same size, what is the area of the window excluding the four openings (1 foot = 12 inches) ?
426 in2
486 in2
529 in2
405 in2
459 in2
426 in2
486 in2
529 in2
405 in2
459 in2
Solution
Length of the window = 3 ft = 36 in
Width of the window = 2 ft = 24 in
Area of the window = 36 × 24 = 864 in2
given, all openings are of equal dimensions.
Let, the length of the opening be = L
Let, width of the opening be = W
given in the figure
3 + W + 3 + W + 3 = 24
Therefore, W = 15/2
3 + L + 3 + L + 3 = 36
Therefore, L = 27/2
Dimensions of the opening is 15/2 by 27/2
Total area of all the four openings = 4 × (15/2) × (27/2) = 405 in2
Area of the window excluding the four openings = 864 − 405 = 459 in2
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