Question

Michelle is buying carpet for a room with the dimensions shown. Michelle calculates that the area she will cover with carpet is 187 1/2 square feet. Explain why Michelle’s reasoning is incorrect, and give the correct area in square feet.

Answer 1

The area of the room is
`147(1)/(2)` square feet so Michelle's reasoning was incorrect.

Explanation:

Step 1:

To calculate the area of the given room, we divide the unknown shape into known shapes.

The room's shape is made of 2 rectangles.

The area of a rectangle is the product of its length and its width.

One rectangle has a length of 10 feet and a width of
`12(1)/(2)` feet.

The other rectangle has a length of
`15-10=5` feet and a width of
`4(1)/(2)` feet.

Step 2:

The area of the first rectangle
`= (10)(12(1)/(2) )= (10)(12.5)= 125` square feet.

The area of the second rectangle
`= (10)(4(1)/(2) )= (5)(4.5)= 22.5` square feet.

The total area of the room
`= 125+22.5 = 147.5 = 147 (1)/(2)` square feet.

The area of the room is
`147(1)/(2)` square feet so Michelle's reasoning was incorrect.