The side of the rhombus is 50 and the diagonal is 80. Find the area of the rhombus.

Given:
rhombus;
a = 50cm – side of the rhombus;
d1 = 80cm – rhombus size
Find: S-?
Solution:
We will search for the area of the rhombus by the formula: S = 1/2 * d1 * d2.
To do this, you need to find the second diagonal of the rhombus d2.
We find it from the equality: (d1) ^ 2 + (d2) ^ 2 = 4 * a ^ 2
80 ^ 2 + (d2) ^ 2 = 4 * 50 ^ 2
6400+ (d2) ^ 2 = 4 * 2500
6400+ (d2) ^ 2 = 10000
(d2) ^ 2 = 10000 – 6400
(d2) ^ 2 = 3600
d2 = 60 cm – the second diagonal of the rhombus.
Then the area of the rhombus S = 1/2 * d1 * d2 = 1/2 * 80 * 60 = 1/2 * 4800 = 2400 sq. Cm.
Answer: S = 2400 sq. Cm.