Question

Find the area of the shaded region. Show all your work.

Answer 1

To find the area of shaded region, we can first find the respective area for the different rectangles.

The area of the larger rectangle:

(3x-4) × (2x+2)

=6x^2 -2x - 8

The area of the smaller rectangle:

(x-3)(x-6)

=x^2 - 9x + 18

We can then deduct the smaller area from the larger area to find the answer:

(6x^2 -2x - 8) - (x^2 - 9x + 18)
= 6x^2 -2x - 8 - x^2 + 9x - 18
= 5x^2 + 7x -26

Therefore, the answer is 5x^2 + 7x -26.

Hope it helps!

Answer 2

Answer with Step-by-step explanation:

The shaded region contains the area of large rectangle excluding the area of smaller rectangle.

i.e. Area of shaded region=Area of large rectangle-Area of smaller rectangle

Area of rectangle=Length×breath

Area of large rectangle=(3x-4)(2x+2)

                                     =3x(2x+2)-4(2x+2)

                                    =6x²+6x-8x-8

                                   =6x²-2x-8

Area of small rectangle=(x-6)(x-3)

                                      =x(x-3)-6(x-3)

                                     =x²-3x-6x+18

                                    = x²-9x+18

Area of shaded region=6x²-2x-8-(x²-9x+18)

                                     =6x²-2x-8-x²+9x-18

Combining like terms, we get

Area of shaded region=5x²+7x-26

Hence, Area of shaded region is:

5x²+7x-26