Example 1 :
Find the perimeter and area of the following figures:
Solution :
In the above figure we have four semi circles and one square. To find the perimeter, we have to add the sum of four semicircles and a square.
Radius = 7/2 => 3.5 cm
Length of each side of square = 7 cm
The perimeter of the given figure
= 4 (perimeter of semicircles) + Perimeter of square
Perimeter of semi circle AEB = Π r
= (22/7) x 3.5
= 22 x 0.5
= 11
Perimeter of 4 semi circles = 4 (11)
= 44 cm
Perimeter of square = 4a
= 28 cm
The perimeter of the given figure = 44 cm + 28 cm
= 72 cm
Area of 1 semi circle = Π r²/2
= (1/2) x (22/7) x (7/2)2
= (1/2) x (22/7) x (7/2) x (7/2)
= (1/2) x 11 x (7/2)
= 77/4
= 19.25 cm²
Area of 4 semi circles = 4 (19.25)
= 77
Area of square = a2
= 7x7
= 49 cm2
Area of given figure
= Area of 4 semi circles + Area of square
= 77 + 49
= 126 cm2
Example 2 :
Find the area of shaded portion.
Solution :
Area of shaded portion
= Area of rectangle - Area of 4 quadrants of circle
Area of rectangle = Length x Width
Length of rectangle = 15 cm
Width of rectangle = 8 cm
= 15 x 8
= 120 cm²
Area of quadrant = Π r²/4
radius of quadrant = 3 cm
= [(22/7) x 3²]/4
= (22 x 3 x 3)/(7 x 4)
= 198/28
Area of 4 quadrant = 4 x 198/28
= 198/7
= 28.28 cm²
Area of shaded portion = 120 - 28.28
= 91.715 cm2
Example 3 :
The kitchen in Mario’s Italian restaurant is 18 meters long and 12 meters wide. A square pantry is connected to the kitchen area. The pantry is 3 meters wide. What is the total area of the kitchen and pantry?
Solution :
Total area of the kitchen and pantry = Area of rectangle + Area of square
Area of rectangle = length x width
Area of square = a x a
Length of rectangle = 18 m and width = 12 m
Side length square pantry = 3 m
Required area = (18 x 12) + (3 x 3)
= 216+9
= 225 square meter
Example 4 :
The area of triangle QTU is 6 square units, and the area of triangle RSU is 6 square units. The dimensions in the figure below are labeled in units. What is the area of triangle STU in square units?
Solution :
Area of triangle SUT
= Area of rectangle TQRS - 2(Area of TQU)
Area of rectangle = length x width
= 6 x 4
= 24 m2
TU2 = TQ2 + UQ2
52 = 42 + UQ2
UQ2 = 25-16
UQ2 = 9
UQ = 3
Area of triangle TQU = (1/2) x base x height
= (1/2) x 3 x 4
= 6
Area of triangles TQU and SRU = 12
Required area = 24 - 12
= 12 m2
Example 5 :
The figure below is divided into four small
squares. The sides of each small square are 6
cm long. What is the area, in square
centimeters, of the entire figure?
Solution :
Area of square = a x a
Side length = 6 + 6 ==> 12 cm
Area of square = 12 x 12
= 144 cm2
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