Final answer:
To find the real-world dimensions of the art studio, a scale factor of 1.25 feet per inch is used, converting the drawing measurements to an actual length of 24 feet and width of 10 feet. The area of the actual studio is then found to be 240 square feet.
Step-by-step explanation:
The student's question involves calculating the real-world dimensions of an art studio from a scaled drawing and then finding its area. According to the drawing plan, the studio is represented by a rectangle measuring 19.2 inches by 8 inches with a scale of 4 inches to 5 feet (4 in.: 5 ft). To find the actual dimensions, we need to calculate the scale factor and apply it to the drawing's measurements.
First, establish the scale factor. The plan's scale of 4 inches: 5 feet can be understood as 4 inches on the drawing equals 5 feet in reality. This gives us a scale factor in the form of a ratio or fraction:
1 inch on the drawing/1.25 feet in reality (since 5 feet divided by 4 inches yields 1.25 feet per inch).
To find the actual length and width:
Actual length: 19.2 inches × 1.25 feet/inch = 24 feet
Actual width: 8 inches × 1.25 feet/inch = 10 feet
After converting the drawing measurements to actual dimensions, we can calculate the area of the studio by multiplying the length by the width:
Area = Length × Width
Area = 24 feet × 10 feet = 240 square feet
Therefore, the actual art studio measures 24 feet by 10 feet, and its area is 240 square feet.