In the adjoining diagram, ABCD and EFGH are squares of side 10 units such that they intersect in a rectangle of 4 units long with diagonal length (CE) = 5 units . Find the total area covered by the squares is:
Since the side of the squares are of 10 units then the area of each square is 100 unit2.
The diagonal of any rectangle of l units long and b units width is sqrt [ l2 + b2].
It is given that sqrt [ l2 + b2] = 5 and l = 4
Then, b2 = 25 - 16 = 9
b = 3 units.
Therefore the area of the rectangle lb = 12 units2.
Then, the total area covered by ABCD and EFGH in adjoining diagram = area of ABCD + area of EFGH - intersecting area between ABCD and EFGH(area of the rectangle)
= 100 + 100 - 12 = 188 unit2 = 188
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