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 $147\frac{1}{2}$ square feet so Michelle's reasoning was incorrect.

Step-by-step 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 $12\frac{1}{2}$ feet.

The other rectangle has a length of $15-10=5$ feet and a width of $4\frac{1}{2}$ feet.

Step 2:

The area of the first rectangle $= (10)(12\frac{1}{2} )= (10)(12.5)= 125$ square feet.

The area of the second rectangle $= (10)(4\frac{1}{2} )= (5)(4.5)= 22.5$ square feet.

The total area of the room $= 125+22.5 = 147.5 = 147 \frac{1}{2}$ square feet.

The area of the room is $147\frac{1}{2}$ square feet so Michelle's reasoning was incorrect.