Geometry : Geometry Exploring Area and Perimeter
By
Sidarth Sekhar Behera
What we will learn : What we will learn Definition of Area, Perimeter and Circumference.
How to find the Perimeter of Square & Rectangle, Triangle, Polygon and Circle.
How to find the area of Squares, Rectangles, Triangles, Polygons and Circles.
Why should we learn : Why should we learn We can use perimeter to know the length of a wire required to fence a rectangular flower bed or plot and circumference to fence a circular ground.
We can use area to know the requirement of plastic sheets to cover a rectangular or circular swimming pool.
Area can be utilized to find the cost of making pathways or borders for circular or rectangular gardens or parks.
Definition of Area, Perimeter and Circumference : Definition of Area, Perimeter and Circumference AREA:- Area is the part of plane or region occupied by the closed figure.
PERIMETER:- Perimeter is the distance around a closed figure.
CIRUCMFERENCE:- Circumference is the distance around a circular region.
PERIMETER and CIRCUMFERENCE : PERIMETER and CIRCUMFERENCE Perimeter of a regular Polygon = number of sides x length of one side
Perimeter of a square = 4 x side
Perimeter of a rectangle= 2x(Length +Breadth)
Perimeter of triangles as a parts of rectangles=Base + Height+ Side
Circumference of Circle= 2πr or πd
where d(diameter)= 2 x r (Radius)
Perimeter of Polygon : Perimeter of Polygon Perimeter
The perimeter of a polygon is the sum of the lengths of all its sides.
Example:
What is the perimeter of a rectangle having side-lengths of 3.4 cm and 8.2 cm? Since a rectangle has 4 sides, and the opposite sides of a rectangle have the same length, a rectangle has 2 sides of length 3.4 cm, and 2 sides of length 8.2 cm. The sum of the lengths of all the sides of the rectangle is 3.4 + 3.4 + 8.2 + 8.2 = 23.2 cm.
Perimeter of Rectangle : Perimeter of Rectangle What is the perimeter of a rectangle having side-lengths of 3.4 cm and 8.2 cm? Since a rectangle has 4 sides, and the opposite sides of a rectangle have the same length, a rectangle has 2 sides of length 3.4 cm, and 2 sides of length 8.2 cm. The sum of the lengths of all the sides of the rectangle is 3.4 + 3.4 + 8.2 + 8.2 = 23.2 cm.
Perimeter of a square : Perimeter of a square What is the perimeter of a square having side-length 74 cm? Since a square has 4 sides of equal length, the perimeter of the square is
74 + 74 + 74 + 74 = (4 × 74) = 296.
Circumference of Circle : Circumference of Circle Circumference of a circle is always more than three times its diameter. This ratio is constant and is denoted by Pi (π )
Pi (π ) approximate value is 22/7 or 3.14.
We can say that C/d= π, Where ‘C’ represents circumference of the circle and ‘d’ its diameter
Or C= πd
we know that diameter (d) of a circle is twice the radius (r) So, C= πd = π x 2r
Circumference of a Circle : Circumference of a Circle Example:
What is the circumference of a circle having a diameter of 7.9 cm, to the nearest tenth of a cm? Using an approximation of 3.14159 for π , and the fact that the circumference of a circle is π times the diameter of the circle, the circumference of the circle is Pi × 7.9 3.14159 × 7.9 = 24.81…cm, which equals 24.8 cm when rounded to the nearest tenth of a cm.
The distance around a circle. It is equal to Pi (π ) times the diameter of the circle. Pi or π is a number that is approximately 3.14159.
Area : Area Area of Rectangle is - Length x Breadth
Area of Square is- Length x Breadth
Area of Parallelogram is - Base x Height
Area of Triangle is – ½(Base x Height)
Area of Circle is – π x r x r (r= radius)
or – ¼ π d x d (d= diameter)
Area of a square : Area of a square If l is the side-length of a square, the area of the square is l × l.
Example:
What is the area of a square having side-length 3.4?The area is the square of the side-length, which is 3.4 × 3.4 = 11.56.
Area of a Rectangle : Area of a Rectangle The area of a rectangle is the product of its width and length.
Example:
What is the area of a rectangle having a length of 6 and a width of 2.2?The area is the product of these two side-lengths, which is 6 × 2.2 = 13.2.
Area of a Parallelogram : Area of a Parallelogram The area of a parallelogram is b × h, where b is the length of the base of the parallelogram, and h is the corresponding height. To picture this, consider the parallelogram below:
We can picture "cutting off" a triangle from one side and "pasting" it onto the other side to form a rectangle with side-lengths b and h. This rectangle has area b × h.
Area of Parallelogram : Area of Parallelogram Example:
What is the area of a parallelogram having a base of 20 and a corresponding height of 7?The area is the product of a base and its corresponding height, which is 20 × 7 = 140
Area of Triangle : Area of Triangle Consider a triangle with base length b and height h. The area of the triangle is 1/2 × b × h.
Area of Triangle : Area of Triangle we could take a second triangle identical to the first, then rotate it and "paste" it to the first triangle as pictured below:
The figure formed is a parallelogram with base length b and height h, and has area b × h. This area is twice that of the triangle, so the triangle has area 1/2 × b × h.
Area of Triangle : Area of Triangle Example:
What is the area of the triangle below having a base of length 5.2 and a height of 4.2?The area of a triangle is half the product of its base and height, which is 1/2 ×5.2 × 4.2 = 2.6 × 4.2 = 10.92..
Area of Circle : Area of Circle The area of a circle is Pi × r2 or Pi × r × r, where r is the length of its radius. Pi is a number that is approximately 3.14159.
Example:
What is the area of a circle having a radius of 4.2 cm, to the nearest tenth of a square cm? Using an approximation of 3.14159 for Pi, and the fact that the area of a circle is Pi × r2, the area of this circle is Pi × 4.22 3.14159 × 4.22 =55.41…square cm, which is 55.4 square cm when rounded to the nearest tenth.
PERIMETER AND AREA : PERIMETER AND AREA THE END
AREA AND PERIMETER : AREA AND PERIMETER THANK YOU
BY
SIDARTH SEKHAR BEHERA