The Correct Answer and Explanation is:
The correct answer is 6,600 square yards.
Explanation:
To find the area of the actual sports field, we must first determine its real life dimensions using the provided scale. The problem gives us the dimensions of a scale drawing and a scale factor that connects the drawing to the actual object. The scale is 1 inch on the drawing represents 20 yards in reality. We will use this information to convert the length and width of the drawing into the actual length and width of the field.
First, let’s calculate the actual length of the sports field. The drawing’s length is 5 ½ inches. To make the calculation easier, we can convert the mixed number 5 ½ to its decimal form, which is 5.5 inches. Using the scale, we multiply the drawing’s length by the scale factor:
Actual Length = 5.5 inches × 20 yards/inch = 110 yards.
Next, we calculate the actual width of the sports field. The drawing’s width is given as 3 inches. We apply the same scale factor to find the real width:
Actual Width = 3 inches × 20 yards/inch = 60 yards.
Now that we have the actual dimensions of the sports field, we can calculate its area. The field is rectangular, so we use the formula for the area of a rectangle, which is Area = Length × Width. Using the dimensions we just found:
Area = 110 yards × 60 yards = 6,600 square yards.
Therefore, the total area of the actual sports field is 6,600 square yards. It is important to scale the dimensions first before calculating the area to arrive at the correct result.
