Question

A rhombus has a perimieter of 8 and diagonal ac equals 2, what is the area of abcd?

Answer 1

Perimeter is 8, rhombus sides are equal. so each side is equal to 2.
Triangle ACD is equailateral triangle. so are of that is: sqrt(3)/4 *(2)^2 = sqrt(3).
We know diagonal of a rhombus bisect that in two equal parts. So area of second part = sqrt(3).

So, area of ABCD = sqrt(3)+sqrt(3) = 2sqrt(3).

Answer 2

@Prateek_agr can't we apply the formula of base x height to find the area?

Answer 3

Can't the area be 2x2 = 4?

Answer 4

Height means perpendicular... Here sides are not perpendicular.
Area of a rhombus = 1/2 *diagonal1*diagonal2.
We know just one diagonal not both of them

Answer 5

Ok, but have a look on this site: http://www.mathopenref.com/rhombusarea.html
It shows an applet to find the area of rhombus, when i dragged the points to lenthgs of 2 for each sides, the applet gives the area as 4

Answer 6

what's about one diagonal there?
there are many rhombus with all sides = 2.

Answer 7

Thanks Prateek!