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A rectangle ABCD has E, F, G and H as mid-points of its sides AB, BC,

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A rectangle ABCD has E, F, G and H as mid-points of its sides AB, BC,  [#permalink]

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New post 15 Aug 2018, 11:15
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A rectangle ABCD has E, F, G and H as mid-points of its sides AB, BC, CD and DA respectively. E, F, G, H are joined to form a quadrilateral EFGH. What is the area of quadrilateral EFGH in square units?

(1) AB = 8 units and BC = 6 units.

(2) GH = 5 units.
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Re: A rectangle ABCD has E, F, G and H as mid-points of its sides AB, BC,  [#permalink]

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New post 15 Aug 2018, 11:36
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amanvermagmat wrote:
A rectangle ABCD has E, F, G and H as mid-points of its sides AB, BC, CD and DA respectively. E, F, G, H are joined to form a quadrilateral EFGH. What is the area of quadrilateral EFGH in square units?

(1) AB = 8 units and BC = 6 units.

(2) GH = 5 units.


As shown in Image,

Let AB = 2x and BC = 2y

Now as ABCD is a rectangle, that is angle A = angle B = angle C = angle D = 90 degrees,

Analyzing Statement 1 -
(1) AB = 8 units and BC = 6 units.

Now we know what is 2x and 2y from this. Subsequently we know x and y,
Therefore we can find area of the four triangles and subtract their sums from the complete rectangle.
This gives us the area of the quadrilateral formed.

Hence Sufficient.

Analyzing Statement 2 -
(2) GH = 5 units

Knowing GH will not help us find the area of the quadilateral . Also it will not help us in finding sides of the rectangle.

Hence Insufficient.

So IMO answer is A
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A rectangle ABCD has E, F, G and H as mid-points of its sides AB, BC,  [#permalink]

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New post 15 Aug 2018, 11:54
amanvermagmat wrote:
A rectangle ABCD has E, F, G and H as mid-points of its sides AB, BC, CD and DA respectively. E, F, G, H are joined to form a quadrilateral EFGH. What is the area of quadrilateral EFGH in square units?

(1) AB = 8 units and BC = 6 units.

(2) GH = 5 units.


The quadrilateral EFGH is a rhombus. (When we joint the midpoints of a rectangle, a rhombus is formed).

Question stem:- Area of the rhombus EFGH?

St1:- AB = 8 units and BC = 6 units.

We have diagonal of rhombus, HF=AB=3 unit & EG=BC=6 unit.

Area of the rhombus EFGH can be determined, Area=0.5*EG*HF
Sufficient.

St2:- GH = 5 units
Only length of sides of the rhombus is given, we need additional information such as angle etc.

Insufficient.

Ans. (A)
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A rectangle ABCD has E, F, G and H as mid-points of its sides AB, BC,   [#permalink] 15 Aug 2018, 11:54
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