If the diagonals of a rhombus are 10 and 24, find the area of the rhombus.

In a rhombus, the diagonals meet at right-angles and also cut each other in two equal halves, like in the picture below.

now, notice the upper-right triangle on the side there, it has a height of 12 and a base of 5, and as you know the area of a triangle is 1/2 bh, so you'd know what the area of that one is.

well, there are 4 equal triangles with that much area, so sum them up, and that's the area of the rhombus.