Question

Kyle wants to put tile in his living room, dining room, and kitchen. How many square feet of tile does he need to buy to cover the entire area if there is a 7 foot by 10 foot island in the middle of the kitchen? Tile can only be sold in multiples of 10 square feet. Do not include units in your answer.

Answer 1

Answer: $800$  (Including the units: $800\ ft^2$)

Step-by-step explanation:

The missing figure is attached.

1. Find the area of the semi-circle with this formula:

$A=\frac{\pi r^2}{2}$

Where "r" is the radius.

You can observe in the figure that the diameter of the semi-circle is:

$d=15\ ft$

Since the radius is half the diameter:

$r=\frac{15\ ft}{2}=7.5\ ft$

Substituting the radius into the formula, you get:

$A_1=\frac{\pi (7.5\ ft)^2}{2}=88.35\ ft^2$

2. The area of a rectangle can be calculated with this formula:

$A=lw$

Where "l" is the length and "w" is the width.

Since the tile won't be put in the island located at kitchen, you need to subtract the area of the smaller rectangle from the area of the larger rectangle. Then:

$A_2=(36\ ft)(20\ ft)-(10\ ft)(7\ ft)=720\ ft^2-70\ ft^2=650\ ft^2$

Therefore, the total area is:

$A_t=88.35\ ft^2+650\ ft^2=738.35$

Since tile can only be sold in multiples of 10 square feet, then he needs to buy  $800\ ft^2$