Plane Figures: The closed 2D shapes are referred to as plane figures.
Closed figure: A figure with no open ends is a closed figure.
Example: Find the Perimeter of the given figure.
Sol: Perimeter = Sum of all the sides
= (12 + 3 + 7 + 6 + 10 + 3 + 15 + 12) m
= 68 m
A rectangle is a closed figure with two pairs of equal opposite sides.
Perimeter of a rectangle = Sum of all sides
= length + breadth + length + breadth
Thus, Perimeter of a rectangle = 2 × (length + breadth)
Example 1: The length and breadth of a rectangular swimming pool are 16 and 12
meters respectively .find the perimeter of the pool.
Sol: Perimeter of a rectangle = 2 × (length + breadth)
Perimeter of the pool = 2 × (16 + 12)
= 2 × 28
= 56 meters
Example 2: Find the cost of fencing a rectangular farm of length 24 meters and breadth 18 meters at 8/ per meter.
Sol: Perimeter of a rectangle = 2 × (length + breadth)
Perimeter of the farm = 2 × (24 + 18)
= 2 × 42
= 84 meter
Cost of fencing = 84 × 8
= Rs. 672
Thus, the cost of fencing the farm is Rs. 672/.
Square is a regular polygon with 4 equal sides.
Perimeter of square = side + side + side + side
= 4 × length of a side
Example: Find the perimeter of a square having side length 25 cm.
Sol: Perimeter of a square = 4 × length of a side
Perimeter of square = 4 × 25
= 100 cm
An equilateral triangle is a regular polygon with three equal sides and angles.
Perimeter of an equilateral triangle = 3 × length of a side
Example: Find the perimeter of a triangle having each side length 13 cm.
Sol: Perimeter of an equilateral triangle = 3 × length of a side
Perimeter of triangle = 3 × 13
= 39 cm
A regular pentagon is a polygon with 5 equal sides and angles.
Perimeter of a regular pentagon = 5 × length of one side
Example: Find the perimeter of a pentagon having side length 9 cm.
Sol: Perimeter of a regular pentagon = 5 × length of one side
Perimeter of a regular pentagon = 5 × 9
= 45 cm
A regular hexagon is a polygon with 6 equal sides and angles.
Perimeter of a regular hexagon = 6 × Length of one side
Example: Find the perimeter of a hexagon having side length 15cm.
Sol: Perimeter of a regular hexagon = 6 × Length of one side
Perimeter of a regular hexagon = 6 × 15
= 90 cm
A regular octagon is a polygon with 8 equal sides and angles.
Perimeter of a regular octagon = 8 × length of one side
Example: Find the perimeter of an octagon having side length 7cm.
Sol: Perimeter of a regular octagon = 8 × length of one side
Perimeter of a regular octagon = 8 × 7
= 56 cm
Area refers to the surface enclosed by a closed figure.
Example: Find the area of the given figure. (1 square = 1 m^{2}).Sol: The given figure is made up of line segments and is covered with some full squares and some half squares.
Full squares in figure = 32
Half squares in figure = 21
Area covered by full squares = 32 × 1 sq. unit = 32 sq. unit.
Area covered by half squares = 21 × (1/2) sq. unit. = 10.5 sq. unit.
Total area covered by figure = 32 + 10.5 = 42.5 sq. unit.
= 20 cm × 12 cm
= 240 sq cm.
To find the length of a rectangle if breadth and area are given:
Example: What will be the length of the rectangle if its breadth is 6 m and the area is 48sq.m?
Sol:
Length = 48/6
= 8 m
To find the breadth of the rectangle if length and area are given:
Example: What will be the breadth of the rectangle if its length is 8 m and the area is 81 sq.m?
Sol:
Breadth = 81/8
= 9 m
Area of a square is the region covered by the boundary of a square.
Area of a square = side × side.
Example: Calculate the area of a square of side 13 cm.
Sol: Area of a square = side × side
= 13 × 13
= 169 cm^{2}.
Area of triangle = (1/2) × base × height = (1/2) × b × h
Example: Find the area of a triangle with a base of 10 units and height of 4 units.
Sol: The formula for the area of a triangle is:
A = (1/2) × base × height.
A = (1/2) × 10 × 4
A = 20 square units
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