Question

a parallelogram whose adjacent sides are 28 cm and 42 cm and one of its diagonals equals to 38 cm find its area

Answer 1

let ABCD be the ll gm where,
AB = 42 cm
BC = 28 cm
AC = 38 cm

In triangle ABC, semi perimeter = (42 + 28 + 38) / 2 = 108 / 2 = 54 cm
so area of triangle ABC = root [s(s-a)(s-b)(s-c)]
= root [54(54-42)(54-28)(54-38)]
= root (54 * 12 * 26 * 16)
= root (9*6 * 6*2 * 2*13 * 16)
= 144 root 13

so area of llgm ABCD = 2 * 144 root 13 [since diagonal divides llgm into 2 equal triangles]
= 288 root 13

also, area of llgm = base * height
or 42 * height = 288 root 13
or height = (288 root 13) / 42
or height = (48/7) root 13 cm