Question

The quadrilateral ABCD is a rhombus with diagonals AC = 12 ft and BD = 4 ft. The points M and N divide diagonal AC on three equal parts. Prove that BMDN is a square and find its area.

Answer 1

area of BMDN 8 ft²

Explanation:

In BMDN the diagonals are BD and MN.

MN is 12/3 = 4 ft long, and BD = 4 ft.

A rhombus with equal diagonals is a square, so BMDN is a square.

In the right triangle BDN, the diagonal BD is the hypotenuse, then:

DN² + NB² = BD²

but DN = NB, then:

2*DN² = 16 ft²

DN² = 8 ft²

The area of BMDN is computed as one of its sides squared. Then, DN² is its area