Q. 54.1( 7 Votes )

# Find the area of a parallelogram given in Fig. 12.2. Also find the length of the altitude from vertex A on the side DC.

Answer :

Area of parallelogram(ABCD) = Area(ΔBCD) + Area(ΔABD)

For Area(ΔBCD),

a = 12, b = 17, c = 25

s = (a + b + c)/2

⇒ s = (12 + 17 + 25)/2 = 54/2 = 27.

Area(ΔBCD) = √s(s-a)(s-b)(s-c)

⇒ Area(ΔBCD) = √27(27-12)(27-17)(27-25)

⇒ Area(ΔBCD) = √27×15×10×2

⇒ Area(ΔBCD) = 90 cm^{2}

As ABCD is a parallelogram, Area(ΔBCD) = Area(ΔABD)

⇒ Area of parallelogram(ABCD) = Area(ΔBCD) + Area(ΔABD)

⇒ Area of parallelogram(ABCD) = 90 + 90

⇒ Area of parallelogram(ABCD) = 180 cm^{2}

Also, Area of parallelogram(ABCD) = CD × (Altitude from A)

⇒ 180 = 12 × (Altitude from A)

⇒ Altitude from A = 15 cm

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