A rhombus has one side length of 10 units. The diagonals of the rhombus differ by 4 units. Find the area of the rhombus.

Question

A rhombus has one side length of 10 units. The diagonals of the rhombus differ by 4 units. Find the area of the rhombus.

Answer 1

Let two diagonals as d1 and d2 and d2=d1+4. Since it is rhombus, two diagonals are bisecting each other. So we can see that 4 congruent right triangles are making this rhombus.

Using Pythagorean Theorem, (d1/2)^2+[(d1+4)/2]^2 = 10^2. We can find d1 = 12 and d2 = d1+4 = 16.

Area of rhombus = d1*d2/2 = 12*16/2 = 96 unit square.

-Hyomin