Area of the window...?

Question

A window is built in the shape of a square with a semi-circle on top. Express the area of
the window as a function of x, the length of a side of the square.

Can you please explain, not much interested in the answer, just want to understand what it is that I'm doing here... thanks

Answer 1

Hello there.



The window area is made up of a square and a semi-circle.



Since the length of the side of the square is x units, the area of the square is x^2 units^2



Since the length of the side of the square is also the diameter of the semi-circle, the area of the semi-circle is 1/2*pi*(x/2)^2 units^2



The area of the windows

= [ x^2 + 1/2*pi*(x/2)^2 ] units^2

= [ x^2 + (pi*x^2)/8 ] units^2



if you wish to factorize the function,



The area of the window = [ x^2/8 ][ 8 + pi ] units^2



Please take note that x^2 means the square of x, or x times x.



Hope this helps. Thank you.

Answer 2

Area of square: x^2

Area of semi-circle: (1/2)(pi)(r^2).

X is also the diameter of the circle, so r, the radius, would be x/2.



So, the total area is:

x^2 + (1/2)(pi)(x/2)^2

Answer 3

To find area use the following formula :



Side * Side