Question

Bella needs to rope off a triangular section of a lake for a swim meet. She leaves the docks in her rowboat, rows for 42 meters in one direction, and places the first buoy. She then rows for 28 meters in a different direction and places the second buoy. If the second buoy is 62 meters from the docks, what is the area of the enclosed triangular region? Round the answer to the nearest tenth.

A. 11.5 square meters
B. 490.7 square meters
C. 9,260.9 square meters
D. 9,299.8 square meters

Answer 1

Using Heron's formula, the area of the triangular region enclosed by Bella is found to be 490.7 square meters. This uses the measurements of the three sides: 42 meters, 28 meters, and 62 meters.

Step-by-step explanation:

To find the area of the enclosed triangular region that Bella needs to rope off, we can use Heron's formula. Heron's formula states that the area of a triangle with sides of length a, b, and c can be found using the formula: Area = √{s(s - a)(s - b)(s - c)}, where s is the semi-perimeter of the triangle, calculated as s = (a + b + c)/2.

In this case, the lengths of the sides of the triangle are 42 meters, 28 meters, and 62 meters. So, the semi-perimeter is: s = (42 + 28 + 62)/2 = 66 meters. Then, the area can be calculated as:

Area = √{66(66 - 42)(66 - 28)(66 - 62)}
√{66 * 24 * 38 * 4}
√{190,272} meters

By calculating the square root, we find that the area is 490.7 square meters. Therefore, the correct answer is B. 490.7 square meters.