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

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Solution

(a) 8 cm²

Let the distance between AB and CD be h cm.
Then ar(||gm APQD) = AP × h
= $\frac{1}{2}$ × AB ×h (AP = $\frac{1}{2}$ AB )
= $\frac{1}{2}$ × ar(||gm ABCD) [ ar(|| gm ABCD) = AB ×h )
∴ ar (||gm APQD) = $\frac{1}{2}$ × 16 = 8 cm²

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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) $12 c m^{2}$

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

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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

(a) 8 cm2 Let the distance between AB and CD be h cm. Then ar(||gm APQD​) = AP ×​ h = 12 ×​ AB ×​h (AP = 12AB ) = 12 ×​ ar(||gm ABCD) [ ar(|| gm ABCD) = AB ×​h ) ∴ ar (||gm APQD​) = 12 ×​ 16 = 8 cm2

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

(a) 8 cm²

Let the distance between AB and CD be h cm.
Then ar(||gm APQD) = AP × h
= $\frac{1}{2}$ × AB ×h (AP = $\frac{1}{2}$ AB )
= $\frac{1}{2}$ × ar(||gm ABCD) [ ar(|| gm ABCD) = AB ×h )
∴ ar (||gm APQD) = $\frac{1}{2}$ × 16 = 8 cm²