How much artificial turi should be purchased to cover an athletic fleld that is in the shape of a trapezoid with a height of $H=11 \mathrm{~m}$ and bases that measure $7=48 \mathrm{~m}$ and $B=36 \mathrm{~m}$ ?
$\mathrm{m}^{2}$

Step 1 ：The problem is asking for the amount of artificial turf needed to cover an athletic field that is in the shape of a trapezoid. The dimensions of the trapezoid are given as a height of \(H=11 \, m\) and bases that measure \(b_1=48 \, m\) and \(b_2=36 \, m\).

Step 2 ：The area of a trapezoid is given by the formula: \[A = \frac{1}{2}(b_1 + b_2)h\] where \(b_1\) and \(b_2\) are the lengths of the bases and \(h\) is the height.

Step 3 ：We can substitute the given values into the formula to find the area of the athletic field. So, \(b_1 = 48m\), \(b_2 = 36m\), and \(h = 11m\).

Step 4 ：Substituting these values into the formula, we get: \[A = \frac{1}{2}(48m + 36m) * 11m = 462.0 \, m^2\]

Step 5 ：Final Answer: The amount of artificial turf needed to cover the athletic field is \(\boxed{462 \, m^2}\)