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jmc

geometry intermediate

Problem

An 8-foot by 10-foot floor is tiled with square tiles of size 1 foot by 1 foot. Each tile has a pattern consisting of four white quarter circles of radius 1/2 foot centered at each corner of the tile. The remaining portion of the tile is shaded. How many square feet of the floor are shaded?
problem
Solution
The four white quarter circles in each tile have the same area as a whole circle of radius , that is, square feet. So the area of the shaded portion of each tile is square feet. Since there are tiles in the entire floor, the area of the total shaded region in square feet is
Final answer
80 - 20\pi