Q17 of 99 Page 269

If the length of one side of a rhombus is 6 cm. and one angle is 60°, then area of field in the shape of rhombus is


∆ABD and ∆CBD are equilateral triangles.


You may know that the height of an equilateral triangle is .side


∴ AO = OC = .AB


=.6


∴ AC (diagonal) = AO+OC


= 6


In ∆AOB, AB2=BO2+AO2


⟹ 36 = BO2 +( .6)2


⟹ BO2=36−27


⟹ BO2 = 9


⟹ BO = 3cm


The diagonal AC = 2×3


= 6cm


Hence, the area of the rhombus=×6×6


=18 sq. cm

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