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, 130 square yards? what would be a good estimate for the new area of the park? the new area of the park would be 130 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, \(l = 10\) yd and \(w=10\) yd. So, \(A_{rectangle}=10\times10 = 100\) square yards.

Step2: Calculate the area of the triangle (approximate the trapezoid - like shape as a triangle for estimation)

The base of the “triangle” is \(b = 6\) yd and the height \(h = 10\) yd. The area of a triangle is \(A=\frac{1}{2}\times b\times h\). So, \(A_{triangle}=\frac{1}{2}\times6\times 10=30\) square yards.

Step3: Calculate the total new area

The total new area \(A = A_{rectangle}+A_{triangle}\). So, \(A = 100 + 30=130\) square yards. But if we consider the actual shape (a trapezoid - like shape which is less than a rectangle of \(6\times10\) when compared to the original full - rectangle assumption for \(130\) (original was maybe a \(10\times13\) rectangle, \(10\times13 = 130\)). The new shape has a part that is a rectangle (\(10\times10\)) and a part that is a triangle (area \(30\) instead of a rectangle \(6\times10 = 60\) if it were the original full - rectangle). So the new area is less than \(130\). A better estimate: assume the non - rectangular part is a trapezoid. But for a simple estimate, if we consider that the non - rectangular part (right part) has an area less than \(6\times10\). If we assume the average of the two parallel sides of the trapezoid (if we consider it as a trapezoid with one side \(0\) (very rough estimate for showing less than) but a better way: original was \(10\times13\) (area \(130\)), new is \(10\times10+\) (area of the other part which is less than \(10\times6\)). Let's say the right part has an area of \(20\) (since it's a triangle - like shape which is half of \(10\times4\) as a better estimate than the previous triangle assumption for showing less). So total \(100 + 20=120\)

Answer:

The new area of the park would be less than \(130\) square yards. A good estimate for the new area of the park would be about \(120\) square yards.