Question

can you help me with question 4, please

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Answer 1

Given: The length of inner rectangle y and breadth x

To find: Write an expression for the area of the shaded region.

Solution:

• Now we have given the dimensions of inner rectangle.

                 Perimeter 1= 2( x + y )

                 Area 1= xy

• Now in figure the dimensions of larger rectangle is not given, but 5 units are increased from all 4 sides, so:

                 Perimeter = 2 ( (x + 10) + (y + 10) ) = 2(x + y + 20)

                 Area 2 = (x + 10)(y + 10) = 2(xy + 10(x + y) + 100)

                 Area of shaded region = Area 2 - Area 1

                 Area of shaded region = 2(xy + 10(x + y) + 100) - xy

                 Area of shaded region = xy + 20(x + y) + 200

Answer:

So an expression for the area of the shaded region is xy + 20(x + y) + 200