Question

a field in the form of parallelogram has one diagonal of 42 M long and the perpendicular distance of this diagonal from either of the outlining vertices is 10 M as shown in the figure find the area of the field

Answer 1

Here ABCD is a parallelogram has one of its diagonal AC = 42 m.

BE ,DF are perpendicular distance from diagonal to the outlying vertices.

BE = DF = 10

Area of parallelogram ABCD = Area of a ΔABC + Area of a ΔACD.

= ( 1/ 2) x AC X BE + (1 / 2) x AC X DF m2

= (1 / 2) x AC [ BE + DF] m2

= (1 / 2) x 42 x [10 + 10] m2

= 420 m2

Answer 2

Diagonal AC = 42m

10 dm=1m.

8dm = 8/10 * m = 0.8m

BE=DF=10 m 8 dm=10.8 r

Area of ||gm ABCD= (Area of AABC) + (Area of Delta ACD)

= 1 2 AC* BE+ 1 2 AC* DF= 1 2 AC(BE+DF)

= 1 2 *42*(10.8+10.8)m^ 2 =(21*21.6)m^ 2 =453.6 m^ 2