The area of the rectangle is the product of its length and its breadth. The area of the shaded region is (2L+2B+4) units².
The area of the rectangle is the product of its length and its breadth.
[tex]\rm \text{Area of rectangle} = Length \times breadth[/tex]
Let the length and breadth of the inner rectangle be L and B.
The area of the reactangle is the product of its length and breadth. Now, the area of the inner reactangle is,
The area of the inner reactangle is = L × B = LB
Now, the area of the outer rectangle with the length of 1 unit increased from both the sides and the breadth by 1 unit from both the sides,
The area of the outer rectangle = (L+2)×(B+2) = LB+2L+2B+4
Further, the shaded region can be found by taking the difference of the rectangles, therefore,
The area of the Shaded region = Area of the outer rectangle - Area of the inner rectangle
The area of the Shaded region = LB+2L+2B+4 - LB = (2L+2B+4)
Hence, the area of the shaded region is (2L+2B+4) units².
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