Calculating Total Surface Area of a Pool with Varying Depths

[Linus]

G'day all I'm new here this is my first post. I just found this forum in hope that you all can help me and I've hopfully come to the right place.

i'm pretty bad at maths (actually shocking at it) and this may be a dumb question but any help would be appreciated. I'm doing total surface area. here's the question

Calculate the total surface area of the inside of the pool?

length of the pool is 27.6 metres
width of the pool is 16.4 metres

The pool has a water depth 1 metre at the shallow end and a depth of 3.2 metres at the deep end .

how do i calculate the total surface area?

Please show working out and explain how you did it. Thanks

 

[Claire84]

Erm, don't take what I say as being right (can be very crap at Maths), but I think that to calculate the length of the side that's unknown in the diagram, you use pythagoras h^2=a^2 + b^2 . h is the side you're looking for and use a=2.4 and b =27.6 (I got the 2.4 from breaking up the side that we're looking at into a rectangle and a triangle and taking he 1 m depth away from the depth at the deeper end of 3.4m). Then once you've worked out that length then you calculate the area of each of the sides, breaking up the side nearest us and the one on the opposite side into a rectangle and a triangle (as before), and calculating their areas that way. Someone please correct me if I'm wrong (and if I am, blame the wine!).

 

[Claire84]

Oh and as for being dumb- no way! If you want dumb you should see half the posts I make (and I'm at uni doing bloody Maths. I figure if the uni people have any sense they should have me out on my ear by the end of this semester!).

 

[Claire84]

Oh, and it is 3.4m depth and not 3.2m, right? If it is 3.2 just use 2.2 instead of the 2.4 I mentioned above.

 

[HallsofIvy]

If Claire84 will forgive me:

"length of the pool is 27.6 metres
width of the pool is 16.4 metres

The pool has a water depth 1 metre at the shallow end and a depth of 3.2 metres at the deep end ."

Okay, the bottom of the pool is a rectangle with length 27.6 metres and width 16.4 metres. Its area is (27.6)(16.4)= 452.64 square metres.

The "deep" end is a rectangle with width 16.4 metres and height 3.2 metres. Its area is (16.4)(3.2)= 52.48 square metres.

The "shallow" end is a rectangle with width 16.4 metres and height 1 metre. Its area is (16.4)(1)= 16.4 square metres.

The sides are trapezoids with "height" (actually the length of the pool) 27.6 metres and two bases of lengths 1 metre and 3.2 metres. The "average" base is (1+ 3.2)/2= 2.1 metres so the area of each side is (27.6)*(2.1)= 57.96 square metres.

Since there are 2 sides, the total area is 452.64+ 52.48 + 16.4 +57.96 +57.96= 637.76 square metres.

 

[Linus]

Thanks for all of your help, i'll now survive another term.