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In the figure above, a circle is tangent to a pair of opposite sides o  [#permalink]

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Question Stats: 65% (01:25) correct 35% (01:27) wrong based on 802 sessions

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In the figure above, a circle is tangent to a pair of opposite sides of a parallelogram. The length of each of these opposite sides is 58 cm. What is the area of the parallelogram in square centimeters?

(1) The perimeter of the parallelogram is 120 cm.

(2) The circumference of the circle is "pi".

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In the figure above, a circle is tangent to a pair of opposite sides o  [#permalink]

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In the figure above, a circle is tangent to a pair of opposite sides of a parallelogram. The length of each of these opposite sides is 58 cm. What is the area of the parallelogram in square centimeters?

(1) The perimeter of the parallelogram is 120 cm.

(2) The circumference of the circle is "pi".

Hi,

Area of parallelogram = Base * height...
Base can be taken either of the parallel sides...
we are given one base as 58, but if you look at the height, it is nothing BUT the diameter of circle as both the opposite sides are tangent to circle..

lets see the statements

(1) The perimeter of the parallelogram is 120 cm.
we know the length of the other side, BUT we cannot deduce the HEIGHT..
Also with All sides known, there can be various types of llgm possible, which will have different areas..
Insuff

(2) The circumference of the circle is "pi".
From the circumference we can find the DIA, which is nothing BUT the height
2*pi*r = pi, SO DIA = 1..
so area = 1*58 = 58
Suff

B
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Re: In the figure above, a circle is tangent to a pair of opposite sides o  [#permalink]

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1
If we modify the original condition and the question, the area of the parallelogram can be found if we find the height of the parallelogram. Hence, we only have to find the diameter of the circle. However, from the condition 2), we get 2r=d(diameter)=1 from 2pi r=pr. The answer is unique and the condition is sufficient. Hence the correct answer is B.

 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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Re: In the figure above, a circle is tangent to a pair of opposite sides o  [#permalink]

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Chetan, I assume by DIA you mean diameter, not diagonal. Could you please explain why 2pr = p? I didn't see how you got to diameter = 1. Thanks!
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Re: In the figure above, a circle is tangent to a pair of opposite sides o  [#permalink]

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2pR=p

p = pi so if we divide p on both sides we get 2R=1

D = 2r, so D = 1.

In this case the diameter is equal to the height of the parallelogram, so base (58) x height (1) = area (58)
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Re: In the figure above, a circle is tangent to a pair of opposite sides o  [#permalink]

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In the figure above, a circle is tangent to a pair of opposite sides of a parallelogram. The length of each of these opposite sides is 58 cm. What is the area of the parallelogram in square centimeters?

(1) The perimeter of the parallelogram is 120 cm.

(2) The circumference of the circle is "pi".

Area of parallelogram = Base*height.

We need to find out height.

(1) The perimeter of the parallelogram is 120 cm.
We can calculate length of other two sides of parallelogram, but not the height. Not Sufficient.

(2) The circumference of the circle is "pi".
If 2 pi r= pi
r=1/2 cm
D= 1 cm, which is height of parallelogram.
Sufficient

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Re: In the figure above, a circle is tangent to a pair of opposite sides o  [#permalink]

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mitko20m wrote:
Chetan, I assume by DIA you mean diameter, not diagonal. Could you please explain why 2pr = p? I didn't see how you got to diameter = 1. Thanks!

1. Yes, mitko20m. DIA is diameter.
2. 2*pi*r = circumference of a circle . This is a direct formula.
circumference of the circle = pi (given in st2.)

Hope it's clear.
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Re: In the figure above, a circle is tangent to a pair of opposite sides o  [#permalink]

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In the figure above, a circle is tangent to a pair of opposite sides of a parallelogram. The length of each of these opposite sides is 58 cm. What is the area of the parallelogram in square centimeters?

(1) The perimeter of the parallelogram is 120 cm.

(2) The circumference of the circle is "pi".

Since we are looking for the area of the parallelogram we need to have a value for the base and the height. We are given a value of 58 for the base from the prompt so we are looking for the height from either statement one or statement 2.

1) The perimeter of the parallelogram is 120cm.- this does not give us any information that would help us find the height so eliminate
2) The circumference of the circle is "pi" - we know that circumference =2pi*r or C=pi*Diameter. From this statement we know that the diameter =1 which means height of the parallelogram is equal to 1. The area of the parallelogram is 58*1 so we know we can solve for the area with this information, therefore statement B is sufficient.
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Re: In the figure above, a circle is tangent to a pair of opposite sides o  [#permalink]

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_________________ Re: In the figure above, a circle is tangent to a pair of opposite sides o   [#permalink] 26 Jan 2019, 00:13
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