Question

An underwater diving area for snorkelers and scuba divers located in a city is designated by buoys and​ ropes, making the diving section into the shape of a trapezoid on the surface of the water. The trapezoid has a height of 265 meters. The bases are 310 meters and 270 meters. Find the area of the diving section.

The area of the diving section is

Answer 1

To find the area of a trapezoid, you can use the formula:

\[
\text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h
\]

where \( b_1 \) and \( b_2 \) are the lengths of the two bases, and \( h \) is the height.

Given:

- \( b_1 = 310 \) meters (the length of the longer base)
- \( b_2 = 270 \) meters (the length of the shorter base)
- \( h = 265 \) meters (the height)

Now, substitute the values into the formula:

\[
\text{Area} = \frac{1}{2} \times (310 + 270) \times 265
\]

First, calculate \( b_1 + b_2 \):

\[
310 + 270 = 580
\]

Now substitute that back into the formula:

\[
\text{Area} = \frac{1}{2} \times 580 \times 265
\]

Now, calculate \( \frac{1}{2} \times 580 \):

\[
\frac{1}{2} \times 580 = 290
\]

Finally, calculate the area:

\[
\text{Area} = 290 \times 265 = 76,850 \text{ square meters}
\]

Thus, the area of the diving section is

\[
\boxed{76,850} \text{ square meters}.
\]