Answer:
(a) The area of the sheet is (9x² - 12x + 4).
(b) The total surface area of the box is x (5x - 4) inches².
Step-by-step explanation:
It is provided that the width and the length of the box are x inches and the height of the box is (x - 1) inches
Then the width of the sheet is:
Width of sheet = (x - 1) + x + (x - 1)
= x - 1 + x + x - 1
= 3x - 2
(1)
The area of the sheet is:
Area of sheet = (3x - 2)² =
= (3x)² - 2 · 3x · 2 + (2)²
= 9x² - 12x + 4
Thus, the area of the sheet is (9x² - 12x + 4).
(2)
The central area, i.e. the base of the box = x²
Each arm folded up = x by (x - 1)
Then the areas of the 4 arms = 4 · x · (x - 1) = 4x² - 4x
Then the total surface area is:
Total Surface Area = Central Area + Areas of the 4 arms
= (x²) + (4x² - 4x
)
= 5x² - 4x
= x (5x - 4) inches²
Thus, the total surface area of the box is x (5x - 4) inches².
