Answer:
1) 12x² -21 ft²Step-by-step explanation:
1)
Height of family room= x
Width of family room= 3x
Length of family room= 3x
The room perimeter is the sum of the lengths of the four walls. The area of the wall, including the door, is the room perimeter multiplied by the height of the room.
gross wall area = (3x+3x +3x+3x).x = 12x²
The area of the door is the product of its height and width.
door area = (7 t)x(3 ft) = 21 ft²
Then,
Area of wallpaper = gross wall area - door area
= 12x² -21 ft²
2)
Height of living room= x
Width of living room= 3x
Length of living room= 5x
Gross wall area = (3x+3x+5x+5x)x = 16x²
Number of doors in living room= 2
Area of one door= 21 ft² (same as family room)
Area of two doors= 2×21 = 42 ft²
Area of wallpaper for the living room= gross wall area - areas of the doors
= 16x² - 42 ft²