The perimeter of the rhombus is 80 and from the corners it is 30 degrees. Find the area of the rhombus.

Given:
ABCD – rhombus,
P avcd = 80,
angle B = 30 degrees.
Find the area S abcd -?
Solution:
1) Consider a rhombus ABCD. His lengths of all sides are equal. Consequently
AB = BC = CD = DA = 80: 4 = 20;
2) Let’s draw the height of the AK;
3) Consider a right-angled triangle ABK. Angle B = 30 degrees. In a right-angled triangle opposite an angle of 30 degrees lies a leg, which is half the hypotenuse. Then
AK = 1/2 * AB;
AK = 1/2 * 20;
AK = 10;
4) Area S abcd = AK * BC;
S abcd = 10 * 20;
S abcd = 200.
Answer: 200.