Answer:
The area of shaded region is: [tex]13x^2+6x-15[/tex]
Step-by-step explanation:
We can see in the diagram that
[tex]Length\ of\ gray\ rectangle = l_g = 3x+5\\Width\ of\ gray\ rectangle = w_g = 4x-3[/tex]
The area of rectangle is given by:
Area = Length * width
Now for gray rectangle
[tex]A_g = l_g * w_g\\= (3x+5)(4x-3)\\= 3x(4x-3)+5(4x-3)\\= 12x^2-9x+20x-15\\=12x^2+11x-15[/tex]
For White Rectangle:
[tex]Length = l = 5-x\\Width = w = x\\A_w = l * w\\A_w = (5-x)(x)\\= 5x-x^2[/tex]
Now,
The area of shaded region will be calculated by subtracting the area of white triangle from the gray triangle.
[tex]A_s = A_g - A_w\\= (12x^2+11x-15) - (5x-x^2)\\=12x^2+11x-15-5x+x^2\\=12x^2+x^2+11x-5x-15\\=13x^2+6x-15[/tex]
Hence,
The area of shaded region is: [tex]13x^2+6x-15[/tex]
