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Question

Mathematics Question on Area of a Polygon

Find the area of a rhombus whose side is 6 cm and whose altitude is 4 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.

Answer

Let the length of the other diagonal of the rhombus be xx.
A rhombus is a special case of a parallelogram.
The area of a parallelogram is given by the product of its base and height.
Thus, area of the given rhombus = Base × Height
= 6 cm × 4 cm
= 24 cm2

Also, area of rhombus = 12\frac{1}{2} (Product of its diagonals)
24 = 12(x×8\frac{1}{2} (x × 8 cm))
x×4=24x × 4 = 24
x=6x = 6 cm

Thus, the length of the other diagonal is 6 cm.