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.

Question

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

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