math question. please help.?

Question

A window has the shape of a semi-circle placed on top of a rectangle.

Express the area A of the window in terms of the width w and height h of the rectangle

Answer 1

let r = radius of the semicircle.

Then r = w/2.

A = (area of semicircle) + (area of rectangle)
A = (1/2)pi*(w/2)^2 + wh
A = (pi/8)*w^2 + wh

Answer 2

One side of the rectangle will equal the diameter of the semi circle. The area of the window, to include the rectangle and the semi circle will be equal to the area of the rectangle (L x W) plus the area of the semicircle, which will be equal to half the side of the rectangle that matches the circle (this will be the radius) squared then times pi, then divided by 2.

Answer 3

This question is not completely clear, as it doesn't say if the semicircle is on the length or the width of the rectangle. You could say it must be along the width, since it says it "on top", but it should be much clearer.

Anyway, if it is along the width, than the diameter of the circle is equal to the width, so the area is (pi(w/2)/2)+(w*L)

Answer 4

You want entire area of the rectangle and a half-circle (ie, semi-circle) area.

For rectangle: A = bh
For full circle: A = pi*r^2, so for half-circle divide by 2.

Sum together for total area.

Answer 5

A=wh+(pi/2(w/2)^2

=wh+pi/8 w^2

Answer 6

wh + (22/7)x(w/2)2

last 2 is square.

1st bracket is value of pie