Question

The shorter diagonal of a rhombus has the same length as a side.

Find the area to the nearest tenth if the longer diagonal is 12 cm. long.

Answer 1

The rhombus could be divided into 2 equal triangles.

Each triangle has 3 sides with same length as shorter diagonal of rhombus(1)

Each triangle has height(H) equal to half of longer diagonal (12cm).

=> H = 12/2 =6cm (2)

Each side of these two triangle has length equal to H x 2/sqrt(3) (property of triangle has 3 same-length sides)

=> Area of rhombus = 2 x Area of triangle = 2 x H x H x 2/sqrt(3) x 1/2 =

= 2 x 6 x 6 x 2/sqrt(3) x 1/2 = ~41.6 (cm2)