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09 Feb 2022, 02:30
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C
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In the figure above, the quarter circle with center D has a radius of 4 and rectangle ABCD has a perimeter of 20. What is the perimeter of the shaded region?
A. \(20 - 8\pi\)
B. \(10 + 2\pi\)
C. \(12 + 2\pi\)
D. \(12 + 4\pi\)
E. \(4 + 8\pi\)
Attachment:
1.jpg [ 8.62 KiB | Viewed 2798 times ]
09 Feb 2022, 03:50
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The perimeter ABCE = AB + BC + EC + AE
From the question stem we know:
white area is a quarter of a circle with center D.
radius = 4 = DC = ED
1) Lets find EC, which will be 1/4th of the circumference of the circle.
Circumference = 2πr = 8π
EC = 8π *1/4 = 2π
2) Find BC.
We know CD = radius = 4 = AB
We know the perimeter is 20.
Perimeter = 2CD + 2BC
20 = 2*4 + 2BC
BC = 6
3) Lets plug in our values and determine the answer.
ABCE = AB + BC + EC + AE
AB = 4
BC = 6
EC = 2π
AE = ?
ABCE = 10 + 2π + AE
Only option is C since we know AE>0.
==> C
If we wanted to calculate AE we can do so but it would only waste time.
AD = BC = 6
ED = r = 4
AE = AD - ED = 2
From the question stem we know:
white area is a quarter of a circle with center D.
radius = 4 = DC = ED
1) Lets find EC, which will be 1/4th of the circumference of the circle.
Circumference = 2πr = 8π
EC = 8π *1/4 = 2π
2) Find BC.
We know CD = radius = 4 = AB
We know the perimeter is 20.
Perimeter = 2CD + 2BC
20 = 2*4 + 2BC
BC = 6
3) Lets plug in our values and determine the answer.
ABCE = AB + BC + EC + AE
AB = 4
BC = 6
EC = 2π
AE = ?
ABCE = 10 + 2π + AE
Only option is C since we know AE>0.
==> C
If we wanted to calculate AE we can do so but it would only waste time.
AD = BC = 6
ED = r = 4
AE = AD - ED = 2
09 Feb 2022, 08:23
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Perimeter of a rectangle = 2*(length +4) = 20, so, length = 6
Perimeter of the shaded part = 6+4 +(6-4)+\(\frac{2*pie*4}{4}\) = 12 + 2*pie
So, I think C.
Perimeter of the shaded part = 6+4 +(6-4)+\(\frac{2*pie*4}{4}\) = 12 + 2*pie
So, I think C.
