Question

Find the area of a rhombus whose each side is 5cm and one of its diagonal is 6cm

Answer 1

In every rhombus, diagonal are perpendicular and bisect each other

Take rhombus as ABCD and bisecting point of diagonals as O

In every rhombus all sides are equal

So AB=BC=CD=DA=5cm

One diagonal is 6cm let AC

OA=OC=3cm

Since it is perpendicular so Pythagorean property applies

(OA)^2+(OB)^2=(AB)^2

=3^2+OB^2=5^2

=9+OB^2=25

=OB^2=25-9=16

=OB=4

Since OB+OD=BD

Then 4cm+4cm=8cm....OB and OD are equal

Area of rhombus=1/2×(d1×d2)

=1/2×(6×8)

=24cm2

I hope it will help you☺