Question

warren is looking to fill a part of a park with sand. the shape below represents the part being covered in sand. how many square yards of the park will warren cover in sand?
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 area of a rectangle is \(A = l\times w\). Here, \(l = 8\) yd and \(w=9\) yd. So, \(A_{rectangle}=8\times9 = 72\) square - yards.

Step2: Estimate the area of the irregular shape

The irregular - shaped part (on the left) has a width of \(4\) yd. If we assume it is approximately a rectangle (for estimation purposes, since it is a rough estimate), and if we consider its height is the same as the height of the other part (\(9\) yd). But since it is a “notched” shape, we can estimate its area. If it were a full rectangle with length \(4\) yd and width \(9\) yd, its area would be \(A = 4\times9=36\) square - yards. But because of the notches, we can estimate it as half of that full - rectangle area. So, \(A_{irregular}\approx18\) square - yards.

Step3: Calculate the total estimated area

The total estimated area \(A_{total}=A_{rectangle}+A_{irregular}\). Substitute \(A_{rectangle}=72\) and \(A_{irregular}\approx18\). So, \(A_{total}\approx72 + 18=90\) square - yards. But since the irregular part is less than a full rectangle (because of the notches), the new area is less than \(90\) square - yards. A better estimate: if we assume the irregular part is about \(12\) square - yards (a more conservative estimate of the “missing” part). Then \(A_{total}=72 + 12=84\) 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 84 square yards.