Find the area of a rhombus if its diagonals are 3.2 cm and 14 cm.

1. The vertices of the rhombus – A, B, C, D. Diagonal AC = 14 cm. Diagonal BD = 3.2 cm. O – the point of intersection of the diagonals.

2. Diagonal ВD divides the rhombus into 2 equal triangles: ΔABC and Δ ВСD.

3. Area ΔАВС = ВD / 2 х AO. AO is the height, since the diagonals of the rhombus are perpendicular.

AO = 1/2 AC = 14: 2 = 7 cm (the diagonals are halved by the point O).

Area ΔABC = 3.2 / 2 x 7 = 1.6 x 7 = 11.2 cm².

4. Area of a rhombus = area Δ ABC x 2 = 11.2 x 2 = 22.4 cm².

Answer: the area of the rhombus is 22.4 cm².