Jensen has an above ground pool in the shape of a regular octagon. Opposite sides are 25 feet apart and each side is 10.4 feet long. It requires 7.5 gallons to fill one cubic foot. How much water is need to fill the pool with 3 feet of water. A. 3900
B. 5850
C. 1560
D. 11700

D

Step-by-step 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.