Question

Find the surface area of the sides and base of this swimming pool. answer is 407

Answer 1

For the base of the swimming pool:

You have the next figures as the sides:

The side number 1 and side 2 are retangles:

`\begin{gathered} A_(s1)=L\cdot W \\ A_(s2)=L\cdot W \end{gathered}`

For the sides 3 and 4 you can draw the side as the sum of a recrtangle and a triangle:

Then, the area of this sides is the sum of the area of the rectangle and the area of the triangle:

`\begin{gathered} A_R=L\cdot W \\ A_T=(B\cdot h)/(2) \\ \\ A_(s3)=(L\cdot W)+(B\cdot h)/(2) \end{gathered}`

You have the next figure as the base:

The area of a rectangle is:

`A_b=L\cdot W`

L is length and w is width

To find the lenght you use the trangle formed in the side 3 and 4:

Pythagoras theorem:

`\begin{gathered} x=\sqrt[]{0.7^2+25^2} \\ x=\sqrt[]{0.49+625} \\ x=\sqrt[]{625.49} \\ x=25.01m \end{gathered}`Then, you have the next areas:Side 1:
`A_(s1)=12m\cdot1.8m=21.6m^2`Side 2:
`A_(S2)=12m\cdot1.1m=13.2m^2`Side 3:
`\begin{gathered} A_(S3)=(25m\cdot1.1m)+(\frac{25m\cdot\text{0}.7m}{2}) \\ \\ A_(s3)=27.5m^2+8.75m^2=36.25m^2 \end{gathered}`Side 4:
`\begin{gathered} A_(S4)=(25m\cdot1.1m)+(\frac{25m\cdot\text{0}.7m}{2}) \\ \\ A_(s4)=27.5m^2+8.75m^2=36.25m^2 \end{gathered}`Base:
`A_B=12m\cdot25.01m=300.12m^2`The total area of the swimming pool is the sum of the areas above, approx. 407 sqare meters