Question

The figure below shows a circular prop with two triangles labeled ABC and AOC made on it. The center of the prop is labeled O.
What is the area of the cloth required to make the circular prop?
Answer

14.14 ft2

28.29 ft2

32.48 ft2

46.58 ft2

Answer 1

I hate this one lol

Answer 2

lol!! ;p

Answer 3

Hmm...I'm not quite sure if I just find the area of the circle or do I need to add the area of triangles as well....
For area of circle...
angle AOC = 2 x 45 = 90 (angle at centre twice angle at circumference)
angle OAC = angle OCA (base angle isos triangle)
= (180 -90)/2 (angle sum of triangle)
= 45
Draw OD such that OD is perpendicular to AC
AD = DC (line joining from centre perpendicular to chord bisects chord)
= 3/2 = 1.5
In triangle ADO
Radius = 1.5 / cos 45 = ...
Area of circle = pi r^2 = ...

In case you also need to find the area of triangle (which I think we need to ) , let me know...

Answer 4

im not really sure to be honest thats just the question i was givin then left to solve aha

Answer 5

Sorry, my mum asks me to do some sewing work.. be back soon!!! I think we need to find the area of triangles..

Answer 6

haha it's k and ok =)

Answer 7

ok continuing on from Callisto
the radius turns out to be 2.855391611
and the area of circle = 25.61422565
and there's no answer for this option so I believe we need to add on the area of the triangles, and then it may be correct.

Answer 8

The central angle is 90 degrees (by the inscribed angle theorem)

So AOC = 90

This means we have a 45-45-90 triangle AOC

Let AO = x

So AC = x*sqrt(2)

3 = x*sqrt(2)

3/sqrt(2) = x

x = 3*sqrt(2)/2

Therefore, the radius of this circle is exactly 3*sqrt(2)/2 units

Answer 9

The area of this circle is then...

A = pi*r^2

A = pi*(3*sqrt(2)/2)^2

A = pi*(9*2/4)

A = (18/4)*pi

A = (9/2)*pi

A = (9/2)*(3.14159)

A = 14.137155


which rounds to 14.14 square feet

Answer 10

Radius = 1.5 / cos 45 = 2.121320344
Area of circle = pi r^2 = 14.13716694 (actually there is an answer :|)

Area of triangle AOC = 1/2 r^2 = 1/2 (4.5) = 2.25
OD = 1.5tan45 = 1.5
BD = r+1.5
Area of triangle ABC = 1/2 (2.121320344 + 1.5) (3) = 5.431980515

Total area = 14.13716694 + 2.25 +5.431980515 = 21.819 (not in option)
So, we just need to find the area of circle :|