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Sun Space

Question

Charlie is helping his family design a sun porch for their house. It will be in the shape of a trapezoid (ABCD), allowing for large windows on several sides. Charlie has labeled the four corners A, B, C, and D. He wants to find out how many 12-inch-square floor tiles he should order if 2 dozen extra tiles are needed for replacements or cutting errors. The tiles come in boxes of 12 tiles per box.

Following is information about the dimensions of the sun porch.

• Line BC is 20 feet long and runs along the living room.
• Line AB is 8 feet long and is perpendicular to line BC.
• Line CD is parallel to line AB but is twice as long as line AB.
• Line AD represents the longest wall with the most windows.
• Line AE is an imaginary line parallel to line BC.
• Point E is on line CD. It is the midpoint of line CD.

How many boxes of floor tiles should Charlie order?