Question

Louise is building a 1:32 scale model of her parents’ office building for a science project. The 1° building has a square floor plan and is twice as tall as it is wide. If Louise’s model is 4 feet tall, what is the area of the full scale building's floors, in square feet?

Answer 1

The area of the full-scale building's floors is 4,096 square feet. We find this by calculating the width of Louise's model (2 feet) and scaling it up by the 1:32 ratio to determine the actual building dimensions, then squaring the width to find the area.

Step-by-step explanation:

Louise is building a 1:32 scale model of an office building. To find the full-scale building's floor area, we must first find the width of the model and then scale it up. Since the model is 4 feet tall and the building is twice as tall as it is wide, the width and depth of the model are both 2 feet. We then apply the scale factor of 1:32 to find the width and depth of the actual building: 2 feet x 32 = 64 feet.

The area of the full-scale building's floor is the width squared, since the floor plan is square. So we calculate: 64 feet x 64 feet to find the area.

Area = width x depth = 64 feet x 64 feet = 4,096 square feet.

Therefore, the area of the full-scale building's floors is 4,096 square feet.