In a rhombus with diagonals 6cm and 8cm, find the side and area.

The side of the rhombus is found by the Pythagorean theorem in one of the equal right-angled triangles, which are formed when the diagonals of the rhombus intersect. The legs in these triangles are equal to half the diagonals.
a = √ ((d1 / 2) ² + (d2 / 2) ²) = √ (9 + 16) = √25 = 5 (cm).
We find the area of the rhombus by the formula:
S = 1/2 * d1 * d2 = 1/2 * 6 * 8 = 24 (cm²).
Answer: a rhombus with a side of 5 cm has an area of 24 cm².