Rectangle RSTU has a perimeter of 42. The half cirde with diameter RS

Question

https://gmatclub.com/forum/download/file.php?id=58592 Rectangle RSTU has a perimeter of 42. The half circle with diameter RS has an area of 8\pi . What is the area of the unshaded part of the figure? A. 104- \pi B. 104- 2\pi C. 104- 4\pi D. 104- 6\pi E. 104- 8\pi Project PS Butler Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS 2020-10-27_12-40-56.png

ShristiBanka · Answer

1. Given perimeter of rectangle: 2(l+b) = 42
 (l+b) = 21

2. Given area of semi-circle = 8π
 Area of circle = 16π = πr^2
 r = 4
 diameter = 8

3. 8 + b = 21
 b = 13

4. Area of rectangle = 13 x 8 = 104

5. Area of unshaded portion = 104 - 8π

Answer: E

rajatchopra1994 · Answer

Explanation:

Rectangle RSTU has a perimeter of 42. i.e. 2(L+B) =42
(L+B) = 21
length is RS which is equal to 2r
The half circle with diameter RS has an area of 8π
i.e. (πr^2)/2 = 8π
r^2 = 16
r = 4
RS = 2x4 = 8
breadth = 21 - 8 = 13

Area of rectangle = 13x8 = 104

Area of Unshaded area = 104 - 8π

IMO-E

Abhishek009 · Answer

\frac{πr^2}{2} = 8π

So,  r = 4

Thus, RS = 8

Further  2 ( 8 + b ) = 42

So, b = 13

Thus, Area of Unshaded region is  13*8 - 8π  , Thus Answer must be (E)

GCMEMBER · Answer

Rectangle RSTU has a perimeter of 42. The half circle with diameter RS has an area of 8π. What is the area of the unshaded part of the figure?

Area of half circle = π(r^2)/2 = 8π
so, r = 4
2r = 8, which is equal to the two of the sides of the rectangle.

Perimeter of rectangle = 42
two of the sides are 8 units each. So, remaining two sides = (42 - 8*2)/2 = 13 each

Area of rectangle = 13*8 = 104

Unshaded area = 104 - 8π

Option E

QuantMadeEasy · Answer

Step 1: Understanding the question 
Area of semicircle =  \frac{1}{2}*(π*r^2) = 8π 
 r^2= 16 ;
r =4 (ignoring -4)
RS = d = 8

Perimeter of the rectangle = 2(RS + ST) = 42;
ST = 13

Step 2: Calculation  
Unshaded portion = Area of rectangle - Area of the semicircle
= (13*8) - 8π
= 104 - 8π

IMO E

Rectangle RSTU has a perimeter of 42. The half cirde with diameter RS

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Rectangle RSTU has a perimeter of 42. The half cirde with diameter RS

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