If ABCD be a rectangle and P, Q, R, S be the mid points of \overrightarrow{AB}, \overrightarrow{BC}, \overrightarrow{CD} and \overrightarrow{DA} respectively, then the area of the quadrilateral PQRS is equal to:

Correct Answer is : 12 area (ABCD)

Mensuration Practice Test 2

Question : 3 of 40

Marks: +1, -0

If ABCD be a rectangle and P, Q, R, S be the mid points of

{AB}↖{→}, {BC}↖{→}, {CD}↖{→}

and

{DA}↖{→}

respectively, then the area of the quadrilateral PQRS is equal to:

Solution:

Given ABCD is a rectangle. P, Q, R, S the mid points of

{AB}↖{→}, {BC}↖{→}, {CD}↖{→}

{DA}↖{→}

PQRS is a rhombus and the area of a rhombus formed by joining the mid points of the sides of a rectangle is half of the area of a rectangle.
ABCD ⇒

1/2

area (ABCD)

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