The closed 2D shapes are referred to as plane figures.
Here “C” is the boundary of the above figure and the area inside the boundary is the region of this figure. Point D comes in the area of the given 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 : 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
Thus, Perimeter of a square = 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
Area refers to the surface enclosed by a closed figure.
To find the area of any irregular closed figure, we can put them on a graph paper with the square of 1 cm × 1 cm .then estimate the area of that figure by counting the area of the squares covered by the figure. Here one square is taken as 1 sq.unit.
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.
Area of a rectangle = (length × breadth)
Example: Find the area of a rectangle whose length and breadth are 20 cm and 12 cm respectively.
Sol: Length of the rectangle = 20 cm
Breadth of the rectangle = 12 cm
Area of the rectangle = length × breadth
= 20 cm × 12 cm
= 240 sq cm.
To find the length of a rectangle if breadth and area are given:
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.
Solution: Area of a square = side × side
= 13 × 13
= 169 cm^{2}.
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