The figures in (a) and (b) below are made up of semicircles and quarter circles; the figure in (c) shows a quarter of a circle in a square. Find the area and the perimeter of each figure in terms of π.

Question

since I can't put a URL to the pic I will try to describe it

1/ a square with the top right corner as A, The bottom right is B, and C is next to B and D is next to A

2/ side DC is 8 in

3/ a diagonal line from B to D

4/ and arc from B to D in triangle ABD

So first of all, I made the 'arc' as part of a circle, by construction, then I found the diameter, circumference, and area. But now I don't know what else to do.

I am only in seventh grade so I don't really understand the topic, my teacher also wants us to make a statement and reason chart. I have a lot of difficulty writing the reason so can you help by showing the chart and "explaining" it, it would be a real help. :)

(I know it's a lot, but if you want you can just show me an equation to find the answer)

Thanks, :)

Answer 1

from 4/
an arc from B to D suggests that the arc passes through A
If that is the case, BD is the diameter and your arc is a half-circle.
(Any angle subtended by a diameter is 90° )
I am going to guess that half the square lies within the half-circle.

If that is the case, we can find BD by Pythagoras:
BD^2 = 8^2 + 8^2
BD^2 = 128
BD = √128 or 8√2
The centre of your half-circle is the midpoint of BD, thus its radius is 4√2
The area of the semicircle is (1/2)π(4√2)^2
= (1/2)π(32)
= 16π

the triangle has area of (1/2)(8)(8) = 32

find any other stuff from here, such as shaded areas, perimeters of whatever

Answer 2

what should I do with the area of the triangle? should I subtract it from the area of the quarter of the whole circle? and to find the perimeter should I find the perimeter of the whole circle then divide it by 4?

thanks for your help Reiny! :)