Help needed calculating the area of a rectangle with 2 semi circles on either side

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da_beast

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Jun 19, 2014
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Help needed calculating the area of a rectangle with 2 arcs on either side

pic20140619163344.jpg

I start University in 3 months and im going over past papers for Mathematics. I have had a good deal of success with all questions bar one.

As i have finished up college i have no lecturers to ask how you would approach this and tbh its annoying me. I have spent 2 days and i feel i have hit a wall

Any help or tips would be appreciated
 
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What i have so far.

Left arc called S1. Right one called S2. The central rectangle area is R

Because i know the diameter of the circle is 4.195 i can calculate the area of the shape if it were a full circle[/COLOR]

I have calculated the full area of the shape if it was a complete circle


A=π r2

d=2r


Solving for
A

A=
1/4 ​
π d2


=
1/4 ​
π4.2 (4.2 squared)

≈13.82146






this needs to be converted to scientific notation but thats not an issue i can do that.

I dont know how to move on from here and calculate the area of S1 and S2 because of the arcs
 
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Denis said:
WHY are you showing all that stuff when all that's being done is the calculation
of the area of a circle with radius = 4.195 / 2?
(pi)r^2 = pi(4.195/2)^2 = 13.821456514422......
Click to expand...

because i also need to calculate the surface area of the top shape on the diagram.

The rectangle with the 2 arcs at the side. I can calculate the rectangle bit but the arced sides im struggling with. If they were complete semi circles then i could use this example to calculate the area of the arced section but because its not a complete semi circle i dont think this following example is applicable.

[h=2]2. Find the area of this portion of a basketball court:[/h][h=2]
pa.4.311.png

This figure is already divided into two shapes: a rectangle and half a circle.
We need to find the area of each and add them together.
pa.4.312.png

pa.4.313.png

pa.4.314.png
.


????????????????
[/h]
 
20140619_205804.jpg

is this along the correct lines?

i need to find the area of the shape at the top of the original diagram posted but because its not a semi circle im not sure how to approach it
 

Would this be relevant?


curve2.gif

In order to calculate the area of a circle segment, you need to first calculate the radius of the circle (r) & the angle theta:
r = (L.L + 4.X.X)/(8.X) and then,
theta = 2arcsin(X/2r)
The formula for surface area is then:
Area(circle segment) =r.r.(theta - sin(theta))/2
This should then be added to the area of the rectangle which is given by:
Area(rectangle) = L.W
 
Denis said:
Where does the 4 and the 8 come from?

Look buddy, brutal honesty: all of your posts so far make no sense,
and all your diagrams are of absolutely no help.
Like, where does the triangle (your 2nd post) come from?

I suggest you start new threads: one thread for each problem.
Post the problems clearly.

We want to help you, but that's impossible if we can't make out what you're asking.

As is, your thread is named:
Help needed calculating the area of a rectangle with 2 semi circles on either side
So you should stick to that in this thread...:idea:
Click to expand...


Yes that other threat was me. im new to this site and wasnt too sure what i was doing.

This picture is all the information i have. i need to calculate the area of the shape at the top of the diagram in my first post.

Ive hit a dead end. i tried to add the 2 ellipses at each end to create one ellipse then use pi* half the 2 axis's and it gave me 13.56 but im sure thats wrong an i need to use triangles.

My old lecturer told me to use triangles???? Im completely stumped
 
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