Answer:
[tex]60\ 000 mm^2[/tex]
Step-by-step explanation:
Refer to the imagine attached.
First of all, let's remember that in a rhombus diagonals are perpendicular to each other, and cut themselves in half. That allows us to focus on 1/4 of the figure (they gray shaded right triangle in my image.
By aplplying pythagorean theorem (or recognizing a 3-4-5 pythagorean triplet scaled up) you can compute the missing side as [tex]3 \times 50 = 150 mm[/tex] long, making the shorter diagonal [tex]300 mm[/tex] long.
At this point you apply the rhombus area formula, with D and d being the two diagonals
[tex]A = \frac12 D\times d = \frac12 400 \times 300 = 60\ 000 mm^2[/tex]
(a bit less than a A4 sheet of paper)
