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?