Answer:
7x - 1
Step-by-step explanation:
Whole rectangle:
Length = x + 5
Width = x - 1
Area of the whole triangle = length × width
= (x + 5) (x - 1)
= x² - x + 5x - 5
= x² + 4x - 5
Unshaded rectangle:
Length = x + 1
Width = x - 4
Area of the unshaded rectangle = length × width
= (x + 1) (x - 4)
= x² - 4x + x - 4
= x² - 3x - 4
Area of the shaded region = Area of the whole rectangle - Area of the unshaded rectangle
= (x² + 4x - 5) - (x² - 3x - 4)
= x² + 4x - 5 - x² + 3x + 4
= 7x - 1
Area of the shaded region = 7x - 1
