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Diagonals of a Rectangle Bisect Each-Other and Are Equal

ABCD is a tra...

Question

$A B C D$ is a trapezium in which $A B ∥ D C, A B = 16 c m$ and $D C = 24 c m$ . If $E$ and $F$ are respectively the midpoints of $A D$ and $B C$ , then $a r (A B F E) = \frac{9}{11} a r (E F C D)$ .

True

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False

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Solution

The correct option is A True
In $Δ A D M$
$\frac{E P}{D M} = \frac{A D}{P M}$
Similarly we get $Q F = 2 c m$
$\frac{E P}{4} = \frac{1}{2}$
$E P = 2 c m$
length of $E F = 20 c m$
area of $(A B F E) = \frac{1}{2} \times (A P) [16 + 20]$
$= 18 A P$
area of $(E F C D) = \frac{1}{2} \times P M (20 + 24)$
$= 22 D M$
area of $(A B F E) = \frac{18 \times a r e a o f (E F C D)}{22}$ [as $A P = P M$ ]
area of $(A B F E) = \frac{9}{11}$ area of $(E F C D)$

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Similar questions

Q. ABCD is a trapezium in which AB || CD, AB = 16 cm and DC = 24 cm. If E and F are respectively the midpoints of AD and BC, prove that ar(ABFE) =

\frac{9}{11}

ar(EFCD).

ABCD is a trapezium in which AB||DC,AB=16 cm and DC=24 cm.If E and Fa re respectively the midpoints of Ad andf BC,prove that $a r (A B F E) = \frac{9}{11} a r (E F C D)$ .

A B C D

is a trapezium in which

A B ∥ D C

M

and

N

are the midpoints of

A D

and

B C

respectively. If

A B = 12 c m; M N = 14 c m

find

C D

Q. In the given Figure,

□

ABCD is a trapezium. AB || DC .Points P and Q are midpoints of seg AD and seg BC respectively.
Then prove that, PQ || AB and PQ =

\frac{1}{2}

( AB + DC ).

Q. In the figure,

□ A B C D

is a trapezium,

A B ∥ D C

. Point

P

and

Q

are midpoints of

s e g A D

and

s e g B C

respectively. Then prove that,

P Q ∥ A B

and

P Q = \frac{1}{2} (A B + D C)

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ABCD is a trapezium in which AB∥DC,AB=16 cm and DC=24 cm. If E and F are respectively the midpoints of AD and BC, then ar(ABFE)=911ar(EFCD).

The correct option is A TrueIn ΔADMEPDM=ADPMSimilarly we get QF=2cmEP4=12 EP=2cmlength of EF=20cmarea of (ABFE)=12×(AP)[16+20] =18AParea of (EFCD)=12×PM(20+24) =22DMarea of (ABFE)=18×area of (EFCD)22 [as AP=PM]area of (ABFE)=911 area of (EFCD)

$A B C D$ is a trapezium in which $A B ∥ D C, A B = 16 c m$ and $D C = 24 c m$ . If $E$ and $F$ are respectively the midpoints of $A D$ and $B C$ , then $a r (A B F E) = \frac{9}{11} a r (E F C D)$ .