YAMT: Precalculus help please... *Solved*

[Ricemarine]

A window is in the shape of a square with a side of length s, with a semicircle of diameter s adjoining the top of the square. Write the total area of the window W as a function of s

The answer should be "(8+pi)s^2 / 8"...

Would someone care to explain how this is to be?... I'm totally lost in this case.

Thanks...

 

[StevenYoo]

first,
the area of the square is s^2 right?

the semicircle on top has a diameter of s, so it has a radius of 0.5s

and the area of that semicircle will be one half the area of a full circle, so the area becomes 0.5*pi*(0.5)^2 or 0.125pi

so the total area is

f(s) = s^2 + 0.125pi

 

[Ricemarine]

Originally posted by: StevenYoo
first,
the area of the square is s^2 right?

the semicircle on top has a diameter of s, so it has a radius of 0.5s

and the area of that semicircle will be one half the area of a full circle, so the area becomes 0.5*pi*(0.5)^2 or 0.125pi

so the total area is

f(s) = s^2 + 0.125pi

Thanks...
I'm just not used to going beyond the boundary of simplifying further...

 

[amol]

1) Draw a diagram. You'll have a square with side s and then a half circle on the top with diameter s.

2) Area of the square. This is simple, it's s ^ 2

3) Area of the half circle. Since the area of a circle is (pi)r^2, this is 1/2 of that. Since diameter = s, radius = s/2. So the area of the semicircle is [(pi)s^2]/8.

4) Add the two areas. To get a common denominator, it's [(pi)s^2 + 8 s^2]/8.

5) Factor out the s^2. You're left with the answer.

edit: DAMN, beaten 😛

edit2: Woohoo, I get credit! 😀

 

[Legendary]

Originally posted by: StevenYoo
first,
the area of the square is s^2 right?

the semicircle on top has a diameter of s, so it has a radius of 0.5s

and the area of that semicircle will be one half the area of a full circle, so the area becomes 0.5*pi*(0.5)^2 or 0.125pi

so the total area is

f(s) = s^2 + 0.125pi

To the OP, the answer given here is both right and matches the answer you want it to be (after distributing and simplifying, you end up with S^2 + pi/8)

 

[Xecuter]

Ugh, can't help you man, I'm just finshing vectors in precalc - no fun.

 

[chuckywang]

s^2 + (s/2)^2*pi/2 = s^2*(1+pi/8)