Question

1. how many 1 - yard - square floor tiles would it take to cover the area shown? dimensions are in yards. corners that look square are square.

Explanation:

Step1: Calculate area of left - hand rectangle

The left - hand rectangle has length 8 yards and width 4 yards. Using the formula for the area of a rectangle $A = l\times w$, we have $A_1=8\times4 = 32$ square yards.

Step2: Calculate area of right - hand rectangle

The right - hand rectangle has length 4 yards and width 2 yards. Using the area formula for a rectangle, $A = l\times w$, we get $A_2 = 4\times2=8$ square yards.

Step3: Calculate area of the semi - circle

The radius of the semi - circle $r = 4$ yards. The formula for the area of a full - circle is $A=\pi r^{2}$, so the area of a semi - circle $A_3=\frac{1}{2}\pi r^{2}=\frac{1}{2}\pi\times4^{2}=8\pi$ square yards.

Step4: Calculate total area

The total area $A = A_1+A_2+A_3=32 + 8+8\pi=40 + 8\pi$ square yards. Since $\pi\approx3.14$, $A\approx40+8\times3.14=40 + 25.12 = 65.12$ square yards.

Step5: Determine number of tiles

Each tile has an area of 1 square yard. So the number of tiles needed is approximately 65 (we take the whole - number part since we can't have a fraction of a tile in a practical sense).

Answer:

65