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Mensuration, Perimeter of an equilateral triangle = 3 × length of a side, Perimeter of a square = 4 × length of a side, In general, perimeter of a regular closed polygon = Number of sides of the polygon ×, length of each side, Example:, If a farmer wants to fence a square field of length 50 m with 5 rounds of wire, then what is the length of the wire required?, Solution:, Length of wire required = 5 × (perimeter of square field), = 5 × (4 × side), = 5 × [(4 × 50) m], = 1000 m, , Perimeter of a rectangle = 2 (length + breadth), Example:, What is the perimeter of a rectangular field whose length and breadth are 15 m, and 8 m respectively?, Solution:, Perimeter of rectangular field = 2 (15 m + 8 m) = (2 × 23) m = 46 m, The distance around a circular region is known as its circumference.
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The circumference of a circle = π × Diameter = 2π × Radius, The value of pi (π) is, , or 3.14., , Perimeter is the length of the boundary of a closed figure., The perimeter of a polygon is the sum of the lengths of all its sides., In case of a triangle ABC, with sides of lengths a, b and c units:, , Perimeter of ABC = AB + BC + AC = a + b + c, The semi-perimeter of a triangle is half the perimeter of the triangle., The semi-perimeter (s) of a triangle with sides a, b and c is, , ., , The semi-perimeter of a triangle is used for calculating its area when the length, of altitude is not known., Area of a rectangle is given by the formula:, Area of a rectangle = length × breadth, Example: How much carpet is required to cover a rectangular floor of length, 25 m and breadth 18 m?, Solution: Area of the carpet required = Area of rectangular floor, = 25 m × 18 m = 450 m2, Area of a square is given by the formula:, Area of a square = side × side
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Example: What is the area of a square park of side 10 m 20 cm?, Solution: Length of park = 10 m 20 cm = 10.2 m, Area of park = 10.2 m × 10.2 m = 104.04 m2, , Area of a triangle:, Area of a triangle =, All the congruent triangles are equal in area, but the triangles having, equal areas may or may not be congruent., Example: ΔABC is isosceles with AC = BC = 6 cm. AE and BD are the, medians and AF = 4 cm. What is the area of ΔABD?, , Solution: In ΔABE and ΔBAD, we have, ], BE = AD, ∠ABE = ∠BAD, [Angles opposite to equal sides], AB = AB, [Common], ⇒ ΔABE, ΔBAD, [By SAS congruency criterion], Area (ΔABE) = Area (ΔBAD), Now, Area ΔABE =, , ⇒ Area ΔABD = 6 cm2, Area of a circle = π × (Radius)2, Example: What is the area of a circle whose circumference is 44 cm?