In the adjoining diagram, the rectangles PQRS and TUVW each with 1 unit width and 3 unit long are arranged such that, they intersect in a square of diagonal(RT) of length 1 unit. The total area covered by the rectangle is:
The breadth(b) and length(l) of the given two rectangles are 1 unit and 3 unit respectively.
Then the area of rectangles(lb) = 1 x 3 = 3 unit2.
Let us find the intersecting area (square of diagonal 1 unit).
We know that the diagonal of any square with side a is a x sqrt(2).
Here, a x sqrt(2) = 1 ==> a = 1 / sqrt(2)
Thus the side of the intersecting area = 1 / sqrt(2) unit.
Then the area of square formed = 1 / 2 unit2.
Therefore, the area covered by the rectangles = area of PQRS + area of TUVW - intersecting area
= 3 + 3 - 1/2 = 11 / 2 unit2.
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