Approximately what is the area of the shaded region above,which is com

Question

https://gmatclub.com/forum/download/file.php?id=38904 Approximately what is the area of the shaded region above,which is composed of a right triangular region and a semicircular region? (A) 4 (B) 5 (C) 7 (D) 8 (E) 10 2017-11-29_0806_003.png

TaN1213 · Answer

imo B

hypotenuse of triangle=  \sqrt{8}  = 2(R)
R=  \sqrt{2} 
area of semicircle = pi( \sqrt{R^2} )/2
=pi
area of triangle = 0.5 *2*2 = 2
total area = pi +2 = 5 approximately

Mick1005 · Answer

IMO :B

Hypotenuse = 2^2 +2^2
=>Hypotenuse= 2root2

Radius of circle= Hypotenuse/2=root2
Area of semi circle= pi* r * r/2= pi
Area of triangle= 1/2 *2 *2= 2

=> Total area= pi+2=2+3.14=5.14~5.

KarishmaB · Answer

The triangle is 45-45-90 triangle so ratio of sides is  1:1:\sqrt{2} 
So length of the hypotenuse is  2*\sqrt{2}  which is also the diameter of the semi circle. Radius =  \sqrt{2}

Total area  = \frac{1}{2}*2*2 + (1/2)*\pi*\sqrt{2}^2 = 5  approximately

Answer (B)

ScottTargetTestPrep · Answer

We see that the triangle is a 45-45-90 triangle, with ratio of side: side: hypotenuse of x: x: x√2. Thus, the hypotenuse of the triangle = 2√2 = diameter of circle, so the radius of the semi-circle is √2.

Thus, the area of the semi-circle is (1/2)*π(√2)^2 = π ≈ 3.14

The area of the triangle is 2 x 2 x 1/2 = 2.

So the total area is 5.14, which is approximately 5.

Answer: B

generis · Answer

If not sure about the shortcuts:

Area of right triangle=  \frac{(b*h)}{2}=\frac{(2*2)}{2}=2  
 
Length of right triangle's hypotenuse,  h  = length of semicircle's diameter,  d

2^2 + 2^2 = h^2 
 8 = h^2 
 \sqrt{h^2}=\sqrt{4*2} 
 h = 2\sqrt{2} =
d

d = 2r ,  2\sqrt{2}=2r ,  r=\sqrt{2}

Area of semicircle: 
  \frac{\pi r^2}{2}=\frac{3.14*(\sqrt{2})^2}{2}=\frac{3.14*2}{2}=3.14

Total area =   2 + 3.14=5.14\approx{5}

Answer B

Madnov2017 · Answer

Approximately what is the area of the shaded region above,which is composed of a right triangular region and a semicircular region?

(A) 4
(B) 5
(C) 7
(D) 8
(E) 10

Show Spoiler

Attachment:

2017-11-29_0806_003.png

[/quote]

Straight B.

Total area= Area of triangle + Area of semicircle
= (1/2)*2*2 + (1/2)*3.14* ((2root2)/2)^2
= 5.14
= 5 (Approx)

Tulkin987 · Answer

10 second approach!
 
The area of the shaded region is slightly more than the area of the square with a side of 2. 
So, the area of the shaded region is slightly more than 2^2=4 leading us to  B .

bumpbot · Answer

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