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The area of the pool that needs to be covered is 960.42 square feet.
What is Pythagoras theorem give example?
- To determine the undiscovered side of a right-angled triangle, utilize the Pythagoras theorem.
- The hypotenuse (third side) of a right-angled triangle, for instance, can be determined using the formula c2 = a2 + b2, where 'c' stands for the hypotenuse and 'a' and 'b' are the two legs.
According to the question:
- We have been given that a community pool that is shaped like a regular pentagon needs a new cover for the winter months.
- To find the area of community pool we will use area of pentagon formula.
- [tex]Area of pentagon=\frac{1}{2} a * p$[/tex] , where, a represents the apothem or perpendicular distance from the center of the pentagon and p represents perimeter of pentagon.
Let us find the perimeter of our given pentagon by multiplying each side length by 5.
[tex]Perimeter of community pool $=5 \times 23.62\\Perimeter of community pool $=118.1$[/tex]
Now let us find apothem of our pentagon by using Pythagoras theorem.
[tex]a^{2}=20.10^{2}-11.81^{2}\\$a^{2}=404.01-139.4761\\$a^{2}=264.5339\\$a=\sqrt{264.5339}\\$a=16.2645$[/tex]
Upon substituting our given values in above formula we will get,
[tex]Area of community pool =\frac{1}{2} \times 16.2645 \times 118.1\\Area of community pool $=8.13224907 \times 118.1\\Area of community pool $=960.418615627971 \approx 960.42$[/tex]
Therefore, the area of the pool that needs to be covered is 960.42 square feet.
Learn more about Pythagoras theorem here:
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