Answer:
D
Explanation:
To solve this question we can use the area formula for an octagon.
It is as follows:
A=2(1+√2)a^2
where "A" is the total area and "a" is the length of a side.
Plug in our side length a=10.4
A=2(1+√2)10.4^2
≈522.24268
Alternatively, you can split the octagon into 8 equal triangles.
The base of each triangle would be 10.4 and the height would be 12.5 since opposite sides are 25 feet apart. (25/2)
The area of a triangle would then be:
A=1/2bh
where "b" is base and "h" is height
A=125*10.4*1/2
=65
Since there are 8 we multiply that by 8 for the area of an octagon
65*8=520
The area of the octagon base is 520 square feet.
I'll use this value to do my calculations as it is more exact.
Now, using this area, we need to find the volume of the pool we are meant to fill.
To do this, we simply multiply the area of the base by the height.
520*3=1560
Now, we know that the volume of the pool is 1560 cubic feet.
Each cubic foot takes 7.5 gallons to fill.
1560*7.5=11700
Therefore, the pool takes 11700 gallons of water to fill.