Question

a field is in the shape of a rhombus has the perimeter 80m and one of its diagonals is 20 m. Find the area of the field.

Answer 1

Answer:

Let PQRS be the field in the shape of a rhombus.

Its perimeter = 400 m.

Length of each of its sides

=(14×400)m=100m.

Let diagonal PR = 160 m.

In ΔPQR, we have

PQ = 100 m, QR = 100 m and PR = 160 m.

Let the lengths of these sides be denoted by a, b, c respectively.

Then, a = 100 m, b = 100 m and c = 160 m.

∴ s=12(100+100+160)m=(12×360)m=180m.

∴ (s−a)=(180−100)m=80m,(s−b)=(180−100)m=80mand(s−c)=(180−160)m=20m.

∴ area(ΔPQR)=s(S−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−−√

=180×80×80×20−−−−−−−−−−−−−−−√m2

=(80×60)m2=4800m2.

Clearly, are (ΔPRS) = area(ΔPQR) = 4800 m2.

Hence, the area of the whole land = (4800 + 4800)m2=9600m2