In a ||gm ABCD,if P and Q are midpoints if AB and CD respectively and ar(||gm ABCD)= $16 c m^{2}$ then ar(||gm~APQD)=?

(a) $8 c m^{2}$

(b) $12 c m^{2}$

(c) $6 c m^{2}$

(d) $9 c m^{2}$

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Solution

ANSWER:
(a) $8 c m^{2}$
Let the distance between AB and CD be h cm.
Then ar(||gm APQD ) = AP × h
= 1/2 × AB × h
(AP = 1/2AB )
= 1/2 × ar(||gm ABCD)
[ ar(|| gm ABCD) = AB × h )
∴ ar ( ||gm APQD ) = 1/2 × 16 = $8 c m^{2}$

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Similar questions

Q. In a || gm ABCD, if P and Q are midpoints of AB and CD respectively and ar(|| gm ABCD) = 16 cm², then ar(|| gm APQD) = ?
(a) 8 cm²
(b) 12 cm²
(c) 6 cm²
(d) 9 cm²

In a parallelogram ABCD, P is a point in interior of parallelogram ABCD. If ar (||gm ABCD) = 18 cm² then [ar ∆APD) + ar(∆CPB)] is :

P,Q,R,S are respectively the midpoints of the sides AB,BC,CD and DA of ||gm ABCD.Show that PQRS is a parallelogram and also show that $a r (| | g m P Q R S) = \frac{1}{2} a r (| | g m A B C D)$ .

Q. In

| | g m

A B C D, E

and

F

are mid-points of sides

A B

and

B C,

a r (B E F) = 10 c m^{2}

then

a r (| | g m A B C D) =

Q. P, Q, R, S are respectively the midpoints of the sides AB, BC, CD and DA of || gm ABCD. Show that PQRS is a parallelogram and also show that

ar (| | gm P Q R S) = \frac{1}{2} \times ar (| | gm A B C D)

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In a ||gm ABCD,if P and Q are midpoints if AB and CD respectively and ar(||gm ABCD)=16 cm2 then ar(||gm~APQD)=? (a) 8 cm2 (b) 12 cm2 (c) 6 cm2 (d) 9 cm2

ANSWER: (a) 8 cm2 Let the distance between AB and CD be h cm. Then ar(||gm APQD ​ ) = AP ×​ h = 1/2 ×​ AB ×​ h (AP = 1/2AB ) = 1/2 ×​ ar(||gm ABCD) [ ar(|| gm ABCD) = AB ×​ h ) ∴ ar ( ||gm APQD ​ ) = 1/2 ×​ 16 = 8 cm2

In a ||gm ABCD,if P and Q are midpoints if AB and CD respectively and ar(||gm ABCD)= $16 c m^{2}$ then ar(||gm~APQD)=?

(a) $8 c m^{2}$

(b) $12 c m^{2}$

(c) $6 c m^{2}$

(d) $9 c m^{2}$

ANSWER:
(a) $8 c m^{2}$
Let the distance between AB and CD be h cm.
Then ar(||gm APQD ) = AP × h
= 1/2 × AB × h
(AP = 1/2AB )
= 1/2 × ar(||gm ABCD)
[ ar(|| gm ABCD) = AB × h )
∴ ar ( ||gm APQD ) = 1/2 × 16 = $8 c m^{2}$