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13 November, 09:00

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.

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  1. 13 November, 09:22
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    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)
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