this is a square with a half circle on top of it... please help.?

Question

A window is in the shape of a square of side s, with a semicircle of diameter s above it. Write a function that expresses the total area of the window as a function of s.

Answer 1

Radius of the circle is s/2, so the area of the full circle would be pi*r^2 = pi*(s/2)^2 = pi*s^2/4. However, it's a semicircle so the area is half as much: (pi*s^2/4)/2 = pi*s^2/8.

The area of the square is just s^2.

So the total area is the sum of those quantities:

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

Or, factored

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

Answer 2

okay, start with the square first.....if each side of the square is s, then use the formula for the area of a square:
A = s^2....so the area of the square is s^2

Now, for the semicircle....we know the diameter is s. For the formula for the area of circle:
A = pi r^2....so we need to first figure out the radius. Well, if the diameter is s, and the radius is 1/2 the diameter, then the radius of our semicircle is s/2. so plug that in for r in the formula:
A = pi (s/2)^2...and when you simplify you get pi times s^2 / 4

BUT, remember that we just found the area of a whole circle...so we need to take half of this for the semicircle...so half of pi times s^2 / 4 will be pi times s^2/8.

So now we have the area of the square and of the semicircle...so we add them together:

A of the window = s^2 + pi(s^2 / 8)

you can simplify this further if you like, but that's the basic idea!

Answer 3

Hmm. The area of a square, side s, is s^2, or s x s.

So, discounting the semi circle we have, s x s.

Pi x r^2 = the area of a circle.

However, we're only dealing with have a circle, and are only given the diameter, s, not the radius.

Therefore, the area of our semi circle is

0.5 x (pi x (0.5 * s)^2) or (pi x (s / 2)^2) / 2.

Therefore, the whole equation goes...

s^2 + (pi x (s / 2)^2) / 2.

Interesting, now we need it as a function of s,

Answer 4

The area of the square is A=s^2

The are of the semicircle is A=π/2 *(s/2)^2
A=π/8 s^2

so the total is
A=(1+π/8)s^2

Answer 5

[(1+pi)/8]s^2

area of square is s^2
area of circle is pi*r^2

We only have half of a circle and r= s/2

so s^2 + [pi* (s/2)^2]/2 is the total area