If a semicircle and triangle are pieced together to form the figure sh

Question

https://gmatclub.com/forum/download/file.php?id=58435 If a semicircle and triangle are pieced together to form the figure shown above, what is the total unit area of the figure? (1) The length of AB is 2 units. (2) x = y 2020-10-18_00-05-22.png

CrackverbalGMAT · Answer

The area of the semicircle can be found as the radius from the figure is 1. We now need to find the area of the triangle ABC

Statement 1:   The length of AB is 2 units.

From this we only get to know that Triangle ABC is isosceles with AB = AC = 2 units.

We cannot find the area of the triangle without knowing the value of the 3rd side (BC)

Therefore Statement 1 Alone is Insufficient  . Answer options could be B, C or E

Statement 2:   x = y

From this, we get that BC = AC = 2 (Sides opposite equal angles)

We cannot find the area of the triangle without knowing the value of the 3rd side (AB)

Therefore Statement 2 Alone is Insufficient  .

Combining Both Statements:

We get that AB = BC = AC = 2. This forms an equilateral triangle and we can find the area of the triangle.

Therefore Both Statements together are sufficient  .

Option C

Arun Kumar

TestPrepUnlimited · Answer

The left side half-circle is fixed, the right side triangle has one side fixed. We need to know 2 more angles on the triangle, 1 angle + 1 length, or 2 more lengths to fix the triangle on the right side.

Statement 1: 
We know only 2 lengths now, insufficient.

Statement 2: 
x = y which leads to AC = BC = 2 but that's still only two lengths, insufficient.

Combined: 
Combined we know all three lengths. The triangle is fixed and we could find the area of it, sufficient.

Ans: C

QuantMadeEasy · Answer

Step 1: Understanding the question 
Area of the semicircle =  \frac{1}{2} *π r^2 = \frac{1}{2} *π 1^2  =  \frac{π}{2}

Area of the figure = Area of the semicircle + Area of the triangle =  \frac{π}{2}  + Area of the triangle

Step 2: Understanding statement 1 alone 
(1) The length of AB is 2 units.
AC = AB = 2, its an isosceles triangle
Area of the triangle cannot be determined
Insufficient

Step 3: Understanding statement 2 alone 
(2) x = y
AC = BC, as sides opposite to equal angle are equal.
Area of the triangle cannot be determined
Insufficient

Step 4: Combining statement 1 and 2 
AB = BC = CA = 2, its an equilateral triangle
Area of the equilateral triangle can be calculated as the side length is known
Sufficient

C is correct

CEdward · Answer

Hi Arun, I am a bit confused.

So for statement 1, you deduced that Triangle ABC is isosceles with AB = AC = 2 units.

However, the only way you could do that is if you assumed angle C is also x.

Statement1 is clearly insufficient.

However, if we can assume that angle C is x in statement 1, why can't we do the same in statement 2?

In which case we know x = y implies that all three angles are 60 degrees thus making statement 2 sufficient.

Can someone explain?

If a semicircle and triangle are pieced together to form the figure sh

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If a semicircle and triangle are pieced together to form the figure sh

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