Q1 of 31 Page 117

One angle of a rhombus is 50° and one diagonal is 5 centimetres. What is the area?

The rhombus ABCD is as shown in the figure shown below,



where,


DB = 5 cm


∠ADC = 50°


We know that,


Diagonals of a rhombus are perpendicular bisector to each other.


Also, diagonals bisect the corner angles of rhombus


So,


∠ODC = 25° [∵ DB bisects ∠D]


OD = 2.5 cm [∵ AC bisects BD]


Now OC is given by,


OC = OD × tan25°


OC = 2.5 × 0.466


OC = 1.166 cm


Also, AC = 2 × OC [∵ BD bisects AC]


AC = 2 × 1.166


AC = 2.332 cm


We know, Area of rhombus =


Area


Area


Area


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