Question

the area of the park being covered in sand changed, as shown below. would this new area of the park be more than or less than the original area of the park, 90 square yards? what would be a good estimate for the new area of the park? the new area of the park would be 90 square yards. a good estimate for the new area of the park would be about square yards.

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\). Here, the length of the rectangle is \(8\) yd and the width is \(9\) yd. So, \(A_{rectangle}=8\times9 = 72\) square yards.

Step2: Estimate the area of the irregular - shaped part

The irregular - shaped part has a width of \(4\) yd. Assume it has a similar height (or length in the non - width direction) as the rectangle part. If we consider it as a rectangle (for estimation purposes), and assume its area is about half of a \(4\times9\) rectangle. The area of a \(4\times9\) rectangle is \(4\times9=36\) square yards. So, an estimate for the irregular - shaped part is \(18\) square yards.

Step3: Calculate the total estimated area

The total estimated area \(A = A_{rectangle}+A_{irregular}\). Substitute the values: \(A=72 + 18=90\) square yards. But since the irregular part is less than a \(4\times9\) rectangle (because of the "notch" in the shape), the actual area is less than \(90\) square yards. A better estimate: assume the irregular part is about a \(3\times9\) rectangle (area \(3\times9 = 27\) square yards less than the original \(4\times9\) full rectangle assumption). So the total area \(A=(8 + 3)\times9=99\) (wrong). Another way: the original area was \( (4 + 8)\times9=108\) (if it was a full rectangle). But because of the "missing" part (the notch). The new area: the rectangle part \(8\times9 = 72\), and the irregular part (if we assume it's equivalent to a \(3\times9\) rectangle). So \(A=(8 + 3)\times9=99\) (no). Let's use another approach. The original area of the full \( (4 + 8)\times9=108\) square yards. If we assume the "notch" in the \(4\) - yd wide part takes away about \(18\) square yards (half of \(4\times9\)). So the new area is \(108-18 = 90\) (but since the notch is more than half). Let's assume the "notch" takes away about \(27\) square yards. So the new area is \(108-27=81\) square yards.

Answer:

The new area of the park would be less than \(90\) square yards. A good estimate for the new area of the park would be about \(81\) square yards.