A rhombus sheet whose perimeter is 32 m and whose one diagnol is 10 cm long ,is painted on both sides at the rate of RS 5 per m^2.Find the cost of polishing.

Since the perimeter of the rhombus is 32m, its side will be 32/4 = 8 m.

(Note that in the question the diagonal should be 10 m and not 10 cm. If the diagonal is 10 cm then the sheet is virtually impossible as the other dimensions are too big.

In any case if you want to solve it for 10 cm then use 10 cm instead of 10 m in the following explanation and you’ll get your answer.)

The figure should look like the following

By Heron’s formula, area of triangle ABC

Also, since diagonal of a parallelogram divides it into two equal parts (or two congruent triangles), we can say that the area of triangle ACD will also be .

Hence, the total area of one side of sheet =

Total area of two sides of the sheet =

Cost = 5× = Rs. 100=Rs. 624.50 approximately.

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