The diagonals AC and BD of a rhombus ABCD are 16cm and 12cm long respectively. Calculate the area of the rhombus.

The diagonals AC and BD of a rhombus ABCD are 16cm and 12cm long respectively. Calculate the area of the rhombus.

Answer Details

In a rhombus, the diagonals are perpendicular bisectors of each other and they divide the rhombus into four congruent right-angled triangles. Therefore, each triangle has a base of 6cm and a height of 8cm (half the length of the diagonals). The area of each triangle is given by: Area = 1/2 x base x height = 1/2 x 6cm x 8cm = 24cm^2 Since there are four such triangles in the rhombus, the total area of the rhombus is given by: Area = 4 x 24cm^2 = 96cm^2 Therefore, the area of the rhombus is 96cm^2, which corresponds to the last option.