Question

The Garden Plan drew a plan for its new garden bed. They used a scale of ½ in : ⅓ yd. Their drawing was a square with 8 inch sides. What would be the area of their actual garden bed?

Answer 1

To determine the actual area of the garden bed from a scale drawing, convert the drawn side lengths to actual lengths using the given scale, then calculate the area. For an 8-inch drawing with a scale of ½ in : ⅓ yd, the actual garden bed has an area of 64 square yards.

Step-by-step explanation:

The student's question relates to scale drawings and converting measurements to calculate the actual area of a garden bed based on the given scale. The scale provided is ½ inch to ⅓ yard. To find the actual dimensions, we first need to convert the 8-inch sides of the drawing to the corresponding length in yards using the scale, then calculate the area.

Step-by-step solution:

1. Convert inches to yards using the given scale: ½ inch is equivalent to ⅓ yard, so 8 inches would be (8 inches) * (⅓ yards/½ inch) = (8 * ⅓) / (½) = 16/1 * ⅓ = 8 yards for one side of the actual garden bed.
2. Since the drawing represents a square, both sides are equal, which means the actual garden bed is 8 yards by 8 yards.
3. Calculate the area by squaring the side length: Area = (side length) ² = 8 yards * 8 yards = 64 square yards.

Therefore, the actual area of the garden bed is 64 square yards.