Question

Find the area of rhombus whose side is 15cm long and altitude is 24cm.​

Answer 1

Once we have y and h , we can compute the area of the triangle like

AΔ=yh2

and subsequently we can have the area of the rhombus like

Ar=2∗AΔ=yh

We’re just missing h .

By definition we have

sin(w)=hx

therefore

h=xsin(w)

from that formula we still don’t have w . We can find it by noting that by definition

cos(w)=y/2x→w=cos−1(y/2x)

and we’re done. Plugging what we just found into the previous formula yields

h=xsin(cos−1(y/2x)) , meaning that the area is given by

Ar=yxsin(cos−1y/2x) .

Now we plug in the values of y and x :

Ar=24∗15sin(cos−1(24/215))

Ar=216