Complete the Problem... For Rhombus PQRS, the diagonals intersect at point T. If the perimeter of the rhombus is 104 units and PT = 10, then what is the area of Rhombus PQRS?

Answer 1

A rhombus is divided into 4 congruent right triangles by its diagonals.

As a rhombus has four equal sides and perimeter 104, each side has length 104/4 = 26

The diagonals meet at T and PT = 10. Consider one of the right triangles, say PTQ.

The hypotenuse, PQ, one of the sides of the rhombus, is the hypotenuse and has length 26, and PT = 10, so TQ, the other leg of the right triangle, has length 24 (the 5-12-13 Pythagorean triple).

Thus, the area of each triangle has area 1/2 * 10 * 24 = 120.

As there are 4 right triangles in the rhombus, the area of the triangle is 4 * 120 = 480.