Find the area of a parallelogram given in Fig.. Also find the length o

1.	Find the area of a parallelogram given in Fig.. Also find the length of the altitude from vertex A on the side DC.
Answer» We know that, Area of parallelogram(ABCD) = Area(ΔBCD) + Area(ΔABD) For Area (ΔBCD), We have, a = 12, b = 17, c = 25 s = (a + b + c)/2 ⇒ s = (12 + 17 + 25)/2 = 54/2 = 27. Area of (ΔBCD) = √s(s-a)(s-b)(s-c) = √27(27-12)(27-17)(27-25) = √27×15×10×2 = 90 cm² Since, ABCD is a parallelogram, Area(ΔBCD) = Area(ΔABD) Area of parallelogram(ABCD) = Area(ΔBCD) + Area(ΔABD) = 90 + 90 = 180 cm² Let altitude from A be = x Also, Area of parallelogram(ABCD) = CD × (Altitude from A) ⇒ 180 = 12 × x ⇒ x = 15 cm

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

Answer»

We know that,

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

For Area (ΔBCD),

We have,

a = 12, b = 17, c = 25

s = (a + b + c)/2

⇒ s = (12 + 17 + 25)/2 = 54/2 = 27.

Area of (ΔBCD) = √s(s-a)(s-b)(s-c)

= √27(27-12)(27-17)(27-25)

= √27×15×10×2

= 90 cm²

Since, ABCD is a parallelogram,

Area(ΔBCD) = Area(ΔABD)

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

= 90 + 90

= 180 cm²

Let altitude from A be = x

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

⇒ 180 = 12 × x

⇒ x = 15 cm