The area of the room is 147.5 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 square feet.