Final answer:
A scale drawing of the park would measure 7 inches by 5 inches on a scale of 1 inch equals 40 yards. The area of the drawing would be 35 square inches, much smaller than the actual park's area, owing to the scale conversion.
Step-by-step explanation:
To create a scale drawing of the park with the given scale where 1 inch represents 40 yards, we simply divide the actual dimensions by the scale factor. The length of the park is 280 yards, and the width is 200 yards. Using the scale, the length in the drawing should be 280 yards / 40 yards per inch = 7 inches. The width in the drawing should be 200 yards / 40 yards per inch = 5 inches.
Now, we'll determine the area of the scale drawing and compare it to the actual park. The area of the scale drawing would be calculated by multiplying the scaled dimensions: 7 inches (length) x 5 inches (width) = 35 square inches. The actual park's area is 280 yards x 200 yards = 56,000 square yards. When we convert the scale drawing's area back into yards using the scale (1 inch = 40 yards), we multiply the area of the drawing in square inches by the scale factor squared, because area is a two-dimensional measurement. So, (1 inch/40 yards) x (1 inch/40 yards) = 1/1600 square yards per square inch. Thus, the scaled area (35 square inches) represents 35/1600 square yards, or 0.021875 square yards. It's clear that the area of the scale drawing is much smaller when compared to the actual park's area due to the scale used.