Areas And Perimeters
This article will clearly explain about the areas and perimeters
. Area of the polygon like square, rectangle, triangle, rhombus, parallelogram etc, is calculated by using the formulas. Area is usually expressed in terms of square units. Perimeter is the sum of sides of the plane or it is sum of the distance around the closed 2D figure of the polygon. Whereas area is the part of the plane occupied by the polygon.This is the definition for the areas and perimeters.The areas are always expressed in square units. Perimeters in given unit itself.
Examples on Areas and Perimeters
Example 1:
The area of a square and a rectangle are equal. If the side of the square is 30 cm and the breadth of the rectangle is 15 cm, find the length of the rectangle. Also, find the perimeter of the rectangle and square.
Solution: Area of square = '(side)^2'
The formula for areas are differ for every shapes and polygon.
= 30 cm 30 cm
= 900 'cm^2'
It is given that, the area of the rectangle = the area of the square
Area of the rectangle = 900 'cm^2' , breadth of the rectangle = 15 cm.
Area of the rectangle = l b
Or 900 = l 15
Or 900/15 =l
l = 60 cm
So, the length of rectangle is 60 cm.
Perimeter of the rectangle = 2 (l + b).
normally perimeters are calculated by adding all the sides of the polygon.
= 2 (60 + 15) cm
= 2 75 cm
= 150 cm
Perimeter of a square = 4 side
= 4 30
= 120 cm.
More Examples on Areas and Perimeters
Find the area of a circle of radius 20 cm (use 'pi' = 3.14).
Solution:
Radius = 20 cm
Area of the circle = 'pi'* r * r
= 3.14 20 20
= 1256 cm2
Example 3:
Find the area of triangle base 10cm and height 5cm?
Solution:
Base (b) = 10 cm, height (h) = 5 cm
Area of the triangle = '(1/2)' (b h)
= ' 1/2' (10 6) cm2
= '1/2' (60) cm2
= 30 cm2.
These are the examples on areas and perimeters.
Check this
Surface Area of a Cone awesome i recently used to see.
A perimeter is the pathway so as to surrounds an area. The word may be used also for the path or its length - it can be the consideration as the distance end to end of the draft of a shape. The perimeter of a circle is called circumference. The perimeter of a polygon is the space around the exterior of the polygon. Perimeter of any polygon is obtained by adding up the measures of the line segments.
Learn Perimeters of Regular Polygons
Equilateral Triangle:
Equilateral Triangle having three equal sides
Perimeter = 3a
Equilateral Quadrilateral (Square or Rhombus):
Equilateral Quadrilateral having four equal sides
Perimeter = 4a
Equilateral Pentagon:
Equilateral Pentagon having five equal sides
Perimeter = 5a
Equilateral Hexagon:
Equilateral Hexagon having six equal sides
Perimeter = 6a
Equilateral Heptagon:
Equilateral Heptagon having seven equal sides
Perimeter = 7a
Regular polygons
Equilateral Octagon:
Equilateral Octagon having eight equal sides
Perimeter = 8a
Equilateral Nonagon:
Equilateral Nonagon having nine equal sides
Perimeter = 9a
Equilateral Decagon:
Equilateral Decagon having ten equal sides
Perimeter = 10a
Equilateral Dodecagon:
Equilateral Dodecagon having twelve equal sides
Perimeter =12a
Examples of Perimeters
Triangle: Perimeter = a + b + c
Rectangle:Perimeter = 2(l + w)
Square:Perimeter = Length of side(a) * four - 4a
Equilateral triangle:Perimeter = Length of side(a) * three= 3a
Equilateral Pentagon:Perimeter = Length of side (a) * 5 = 5a
Ex 1: What is the perimeter of a triangle whose sides are 3 centimeters, 5 centimeters and 7 centimeters.
Sol: Step I: Perimeter = 3 cm + 5 cm + 7 cm
= 15 cm
Ex 2: A rectangle has a length of 7 centimeters and a breadth of 5 centimeters. Find the perimeter.
Sol: Step I: Perimeter = 2 (l + b)
Step II: = 2 (7 + 5)
Step III: = 2 (12)
= 24 cm
Ex3: What is the perimeter of a square with both side measuring 30 inches.
Sol: Step I: Perimeter = 4a
Step II: = 4 * 30
= 120in
Ex 4: What is the perimeter of an equilateral triangle with both side measuring 12 centimeters.
Sol: Step I: Perimeter = 3a
Step II: = 3 * 12
= 36 cm
Ex 5: What the perimeter of a regular pentagon with both side measuring 7 inches.
Sol: Step I: Perimeter = 5a
Step II: = 5 * 7
= 35 in
by: mathqa
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