Area of a Shape

Question

A cathedral window is built in the shape of a semicircle. If the window is to contain three stained glass sections of equal size, what is the area of each stained glass section? Express answer to the nearest square foot.

There is obviously something missing. Is this window the size of peanut or the size of an elephant? By "size", do you mean "area"? — MPW, Jul 13 '14 at 16:23
@MPW Yes, they would mean area. It would simply depend on radius. — Rivasa, Jul 13 '14 at 16:24
Even if you have more information you are likely to have to ignore the area of the structures which separate the sections. — Mark Bennet, Jul 13 '14 at 16:25
@IHeartBunnies check my hint, you would want to solve in terms of r, if it doesn't give you a picture/more info. — Rivasa, Jul 13 '14 at 16:25
@MarkBennet This seems like an ideal question, so I would assume the separator is infinitly thin. — Rivasa, Jul 13 '14 at 16:26

score 2 · Answer 1 · answered Jul 13 '14 at 16:23

2

Area of a circle is $\pi r^2$, since we are talking about a semicircle, this is just $$\frac {\pi r^2}{2}$$

Since this semicircle is further divided into 3 sections, divide the area of the semicircle into 3, thus

$$\frac {\pi r^2}{6}$$

answered Jul 13 '14 at 16:23

JoeyAndres

1,269

You've given the only possible answer, given the incomplete nature of the question. – MPW Jul 14 '14 at 01:01

score 1 · Accepted Answer · answered Jul 13 '14 at 16:22

1

Hint: The area of a circle is $A= \pi r^2$, then what is the area of a semi-circle? What if you divide that in three parts?

Edit: If it is asking without more context, I suspect it wants area in terms of $r$?

answered Jul 13 '14 at 16:22

Rivasa

1,575

score 0 · Answer 3 · answered Jul 20 '17 at 09:15

The question could have been more interesting if the width of each shutter in the semicircular arch was to be determined. The areas of the three shutters are assumed to be equal. and the shutters have perfectly vertical frames of negligible thickness.

Area of a Shape

3 Answers3