Answer:
a. The area of the wall is 60 ft.²
b. The minimum length of wallpaper to be purchased is 30 ft
Explanation:
a. The given diagram is a pentagon, with the two vertical sides equal in length and the two slant sides equal in length and one horizontal
The length of the vertical sides = 6 feet each
The length of the horizontal side = 8 feet
The height of the pentagon = 9 feet
The pentagon can be split into a rectangle with a triangular cap by an horizontal line drawn at point of intersection of the vertical sides and the horizontal sides
The area of the formed rectangle = Base × Height of rectangle
∴ The area of the formed rectangle = 6 × 8 = 48 ft.²
The area of the triangular part of the figure = 1/2 × base × Height of triangle
a = 9 - 6 = 3 feet
∴ The area of the triangular part of the figure = 1/2 × 8 × 3 = 12 ft.²
The area of the wall = The area of the formed rectangle + The area of the triangular part of the figure
∴ The area of the wall = 48 ft.² + 12 ft.² = 60 ft.²
The area of the wall = 60 ft.²
b. The width of the sold wallpaper = 2 feet wide
The area of wallpaper = Length of wallpaper × The width of the sold wallpaper
The area of wallpaper required = The area of the wall = 60 ft.²
∴ 60 ft.² = Length of wallpaper × 2 ft.
Length of wallpaper = 60 ft.²/2 ft. = 30 ft.
The minimum length of wallpaper to be purchased = 30 ft.