I redraw one of the triangles on my attachment.
Ratio of cos is ratio that compares the side adjacent to the angle with the hypotenuse. It could be write as:
cos θ = height/hypotenuse
cos θ = h/x
x cos θ = h
Ratio of sin is ratio that compares the side in front of the angle with the hypotenuse. It could be write as:
sin θ = base/hypotenuse
sin θ = b/x
x sin θ = b
Determine the area of rhombus
Because the four triangles are congruent, we can calculate the area by multiplying one of triangle area by 4
a = 4 × area of triangles
a = 4 × 1/2 × b × h
a = 4 · 1/2 bh
Input b and h as the trigonometry ratio
a = 4 × 1/2 × b × h
a = 2 × b × h
a = 2 × x sin θ × x cos θ
a = 2x² cos θ sin θ
Answer
[tex] A_{r} =\boxed{4} \frac{1}{2} bh[/tex]
[tex]A_{r} =\boxed{2 x^{2} }cos \alpha sin \alpha [/tex]
