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Perimeter of the shaded region

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by gmattesttaker2 » Sat Feb 22, 2014 1:15 am
Hello,

Can you please assist with this:

In the figure above, arcs PR and QS are semicircles with centers at Q and R respectively. lf PQ = 5, what is the perimeter of the shaded region?

OA: 10 pi + 10

I am getting 10pi though.

Thanks,
Sri
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by Uva@90 » Sat Feb 22, 2014 1:36 am
gmattesttaker2 wrote:Hello,

Can you please assist with this:

In the figure above, arcs PR and QS are semicircles with centers at Q and R respectively. lf PQ = 5, what is the perimeter of the shaded region?

OA: 10 pi + 10

I am getting 10pi though.

Thanks,
Sri
Sri,
Perimeter of a mentioned diagram is,
perimeter of PR+ Perimeter of RS+ Perimeter of SQ+ Perimeter of QP

perimeter of PR =pi*r =5*pi
Perimeter of RS = 5
Perimeter of SQ = pi*r =5*pi
Perimeter of QP =5

Hence total is 10*pi +10

Regards,
Uva.
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by [email protected] » Sat Feb 22, 2014 6:04 pm
Hi Sri,

Uva has properly explained the "math" behind the question. Here's the "pattern" behind the concept.

Since we're dealing with 2 semi-circles, and QR represents the same radius in both of them, we know that the 2 semi-circles are identical. The perimeter of the shape is made up of....

The circumference of the full circle + the diameter of that circle.

Since the radius = 5, we know....
Circumference = 2r(pi) = 10pi
Diameter = 2r = 10

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