bandzswagg123
15.04.2021 •
Mathematics
Mr. Dieter wants to tile the family room in his basement. He has selected a pattern of square tiles that measure 9 inches by 9 inches each. The shape of the floor to be tiled is shown below. a. What is the area of the family room in square feet? b. How many of the 9 inch by 9 inch tiles will it take to cover the floor? (NOTE: You will need to convert the area in Part a from square feet to square inches.) c. If the tile is sold only in boxes of 12 tiles per box, how many boxes will Mr. Dieter have to buy to tile the family room?
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Ответ:
146 ft²
21.6 tiles
1.8 boxes
Step-by-step explanation:
Please find attached an image of the family room used in answering this question
the family room has the following shapes : 2 triangles and one rectangle
the area of the family room can be determined by calculating the area of each of the shape and adding the 3 areas together
area of a rectangle = length x breadth
16 x 7 = 112 ft²
Area of a triangle = 1/2 x base x height
Area of the smaller triangle = (1/2) x 4 x 3 = 6 ft²
Area of the bigger triangle = (1/2) x 8 x 7 = 28 ft²
Sum of the areas = 112 + 6 + 28 = 146 ft²
b.
1. First convert the area of the room to inches
1 ft = 12 in
146 x 12 = 1752 in²
2. the next step is to determine the area of the tile
area of a square = length²
9² = 81 in²
3. Divide the area of the room by the area of the tile
1752 / 81 = 21.6 tiles
c. total number of boxes that would be bought = 21.6 /12 = 1.8 boxes
Ответ: