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505-555 (Easy)|   Geometry|      
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Bunuel
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In the figure above, arcs PR and QS are semicircles with centers at Q 28 Nov 2017, 21:19
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In the figure above, arcs PR and QS are semicircles with centers at Q and R respectively. If PQ = 5, what is the perimeter of the shaded region?

(A) 5π + 5
(B) 5π + 15
(C) 10π + 10
(D) 10π + 15
(E) 100π

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C
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In the figure above, arcs PR and QS are semicircles with centers at Q 28 Nov 2017, 22:42
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The radius of both the circles is equal and is 5 . Hence, the total perimeter is equal to 2πR+2R.
Hence the perimeter is equal to 10πr+10.
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In the figure above, arcs PR and QS are semicircles with centers at Q 30 Nov 2017, 16:21
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Bunuel

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

(A) 5π + 5
(B) 5π + 15
(C) 10π + 10
(D) 10π + 15
(E) 100π

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Attachment:
2017-11-29_0807.png
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Because semicircle PR is centered at Q, its radius = QR = PQ (given) = 5. Because semicircle QS is centered at R, its radius, too, is QR = 5.

Perimeter:

Segment PQ = 5
Segment RS = 5

Arc PR = \(\frac{2πr}{2}=\frac{10π}{2}= 5π\)

Arc QS = \(\frac{2πr}{2}=\frac{10π}{2}= 5π\)

Total: 10 + 10π

Answer C
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In the figure above, arcs PR and QS are semicircles with centers at Q 30 Nov 2017, 20:17
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Bunuel

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

(A) 5π + 5
(B) 5π + 15
(C) 10π + 10
(D) 10π + 15
(E) 100π

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2017-11-29_0807.png
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we have r = 5 for each circle
perimeter of half circle = Pi * r

so perimeter of the shaded region = perimeter of both half circles + r1 + r2 = 2*5*pi + 5 + 5 = 10pi + 10
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In the figure above, arcs PR and QS are semicircles with centers at Q 01 Dec 2017, 07:53
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Bunuel

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

(A) 5π + 5
(B) 5π + 15
(C) 10π + 10
(D) 10π + 15
(E) 100π

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We see that the radii of both semicircles is 5.

Thus, the semicircular arc of each semicircle (half circumference) is 1/2 x 2π(5) = 5π. We also see that PQ = RS = 5. Thus the perimeter of the shaded region is:

5π + 5π + 5 + 5 = 10π + 10

Answer: C
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In the figure above, arcs PR and QS are semicircles with centers at Q 20 Mar 2018, 11:52
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Hi All,

There's a great "pattern" behind this question.

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. Thus, the perimeter of the shape is made up of….

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

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

Final Answer:
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C

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In the figure above, arcs PR and QS are semicircles with centers at Q 15 Aug 2023, 03:28
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