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James is fencing off a triangular region for his cats to play in. From the first fence post, he walks 13 meters in a straight line and plants the second fence post. From there, James heads in another direction for 5 meters and places the third fence post. If the distance between the first and third fence posts is 9 meters, find the area of the enclosed region. Round the answer to the nearest tenth.


A.

5.2 square meters

B.

16.1 square meters

C.

385.9 square meters

D.

386.9 square meters

Verified Answer :

JcAlmighty

The answer is B. 16.1 square meters

The region has triangular shape. To calculate the area of the triangle when three sides are known, we will use the Heron's formula:
A = √s(s-a)(s-b)(s-c)
where:
A - the area of the triangle
a, b, and c - the sides of the triangle
s - half of the triangle's perimeter: s = (a+b+c)/2

It is given:
a = 13 m
b = 5 m
c = 9 m

First, calculate s:
s = (a+b+c)/2 = (13+5+9)/2 = 13.5

Now, it is easy to calculate the area:
A = √s(s-a)(s-b)(s-c) = √13.5(13.5-13)(13.5-5)(13.5-9) = √13.5×0.5×8.5×4.5 = √258.19 = 16.07 ≈ 16.1

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