1. In a rhombus, the diagonals bisect each other at right angles. So you have 4 congruent right-angled triangles with sides 5 and 12, and the hypotenuse is the side of the rhombus.
s^2 = 5^2 + 12^2
(You should recognize that Pythagorean triple, if not, remember it)
Find the area of one triangle, then multiply by 4
2. There are 6 identical isosceles triangle with a base of 24/6 or 4 units, and a central angle of 60°
The length of those sides is your radius.
3. I drew a figure ABCD , with AD || BC
AD = 10
AB = 20
BC = 30, and
CD = 10
From A draw a line AP, so that AP is || to DC and P is on BC
So AP=10 and APCD Is a rhombus (all sides = 10)
Now look at triangle ABP , it is isosceles with sides 20,20, and 10
We need an angle, I found angle APB
cos APB =5/20
angle APB = appr 75.52°
So angle APC = 104.48°
Take it from there.