A rectangle is a special case of a parallelogram in which each pair of adjacent sides is perpendicular.
To find area and perimeter of the rectangle, we use the formulas given below.
Area of rectangle = length x width
Perimeter of rectangle = 2 (length + width)
Example 1 :
Find the perimeter of the rectangle.
Solution :
Length = 7 m and width = 3 m
Perimeter of the rectangle = 2(7+3)
= 2(10)
= 20 m
So, perimeter of the rectangle is 20 m.
Example 2 :
Find the area of rectangle given below.
Solution :
Length = 2.5 m and width = 1.4 m
Area of rectangle = length x width
= 2.5(1.4)
= 3.5 m^{2}
So, area of rectangle is 3.5 m^{2}.
Example 3 :
Find the area and perimeter of the rectangle given below.
Solution :
length = 2x and width = x
Area of rectangle = length ⋅ width
= 2x(x)
= 2x^{2}
So, area of rectangle is 2x^{2} meter square.
Perimeter of the rectangle = 2(length + width)
= 2(2x+x)
= 2(3x)
= 6x
So, perimeter of the rectangle is 6x meter.
Example 4 :
A rug measuring 2.5 m by 3.5 m was placed in a room 6.4 m long and 8.2 m wide. What area of floor is not covered by the rug?
Solution :
Length of the room = 6.4 m and width = 8.2 m
Length of rug = 3.5 m and width = 2.5 m
Area of the hall = 6.4(8.2)
= 52.48 m^{2}
Area covered by rug = length ⋅ width
= 3.5(2.5)
= 8.75 m^{2}
Area is not covered by rug = 52.48-8.75
= 43.73 m^{2}
Example 5 :
A brick wall will be built 56 m long and 10 bricks high. If each brick is 20 cm long, how many bricks will be needed?
Solution :
Length of wall = 56 m
1 m = 100 cm
56 m = 5600 cm
5600/20 ==> 280
280 bricks are needed.
Example 6 :
The school sports fields are laid out in a rectangle 220 m by 160 m. Find the cost of fertilizing the grass if 1 kg of fertilizer covers 80 square meters and fertilizer costs $25 for a 40 kg bag.
Solution :
Area of rectangular field = length x width
Length = 220 m and width = 160 m
Area of field = 220(160)
= 35200 square meter
1 kg of fertilizer covers 80 square meters
= 35200/80
= 440
Cost of 40 kg bag = $25
To number how many 40 kg bags are needed = 440/40
= 1 1 bags
Cost of 1 bag = $25
Required cost = 11(25)
= $275
Example 7 :
A carpet measuring 4 m by 3 m is placed in a room 5.2 m long and 4.8 m wide. What area of the floor is left uncarpeted?
Solution :
Length of room = 5.2 m, width = 4.8 m
Length of carpet = 4 m and width = 3 m
Area of room = 5.2(4.8)
= 24.96 square meter
Area covered by carpet = 4(3)
= 12 square meter
Area of floor is left uncarpeted = 24.96 - 12
= 12.96 square meter
Example 8 :
A lounge room is 5.4 m long, 4.8 m wide, and 4.2 m high. It has a door 2 m by 1 m and a window 2 m by 1.5 m.
a) Draw a diagram to illustrate the room.
b) If wallpaper costs $5.50 per square meter, find the cost of wallpapering the four walls.
Solution :
(a)
(b) From the picture :
Area of wall in the left side :
= (4.8)(4.2) ==> 20.16 ---(1)
Area of wall in the back side :
= (5.4)(4.2) ==> 22.68 ---(2)
Area of wall in the front face except door :
= 5.4(4.2) - 2(1)
= 22.68-2
= 20.68 square meter ---(3)
Area of wall right side except the window :
= 4.8(4.2) - 2(1.5)
= 20.16-3
= 17.16 square meter ---(4)
Area covered by wall paper
= 20.16 + 22.68 + 20.68 + 17.16
= 80.68 square meter
Cost of covering 1 m = $5.50
Required cost = 80.68(5.50)
= $443.74
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