Calculate the area of a rhombus if one of its diagonal is 12 dm and the second diagonal is 9 dm.

1. The tops of the rhombus – A, B, C, D. Diagonal AC = 12 dm. Diagonal ВD = 9 dm. О is 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 = 12: 2 = 6 dm (the diagonals are halved by the point O).

Area ΔABC = 9/2 x 6 = 4.5 x 6 = 27 dm².

4. Area of a rhombus = area Δ ABC x 2 = 27 x 2 = 54 dm².

Answer: the area of the rhombus is 54 dm².