Question

warren is looking to fill a part of a park with sand. the shape below represents the part of the park 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?4 yd8 yd9 ydthe new area of the park would be □ 90 square yards.less thanmore thana good estimate for the new area of the park would be about □ square yards.

Explanation:

Step1: Calculate full rectangle area

The full rectangle has length $4+8=12$ yd and width $9$ yd.
Area: $12 \times 9 = 108$ square yards

Step2: Estimate removed partial area

The left partial shape is roughly half of a $4 \times 9$ rectangle.
Estimated removed area: $\frac{1}{2} \times 4 \times 9 = 18$ square yards

Step3: Compare new area to 90

New area = $108 - 18 = 90$? No, the removed shape is less than half, so new area is less than 108, and since the removed part is ~18, but visually it's slightly less than half, so new area is less than 90? Wait, correction: original full area is 108, original sand area was 90, so the removed part was 18. The new shape has more removed, so new area is less than 90.

Step4: Estimate new area

The new removed part is ~$\frac{3}{4}$ of $4 \times 9$, so removed area $\approx \frac{3}{4} \times 36 = 27$. New area $\approx 108 - 27 = 81$, so a good estimate is 80-85, we use 80 or 81, 80 is a simple estimate.

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 80 square yards.