Table of contents  
Area of Parallelograms  
Area of Triangle  
Circles  
Circumference of Circle 
To cover the boundaries of a garden with flowers, you need to calculate the perimeter. The perimeter is the total distance around the garden. Example: For a rectangular garden, add up all the sides:
The area is the amount of space inside a shape. For a rectangle, it is found by multiplying the length by the width.
Example: For the same rectangle:
A parallelogram is a twodimensional geometrical shape whose sides are parallel to each other. It is a type of polygon having four sides (also called quadrilateral), where the pair of parallel sides are equal in length.
To find the area of a parallelogram, you can follow these steps:
Example Calculations:
Example 1: If you have a parallelogram ABCD, where AB is the base and DE is the height (perpendicular to AB), then the area would be given by:
Parallelogram ABCD
Area of parallelogram ABCD = Base × Height= AB x DE
Example 2: Find the area of the following parallelograms:
Ans: Base = 8 cm
Height = 3.5 cm
Area of parallelogram = Base × Height
Area of parallelogram = 8 cm x 3.5 cm = 28 cm^{2}
Ans: Base = 8 cm
Height = 2.5 cm
Area of parallelogram = Base × Height
Area of parallelogram = 8 cm x 2.5 cm = 20 cm^{2}
Example 3: PQRS is a parallelogram. QM is the height from Q to SR and QN is the height from Q to PS. If SR = 12 cm and QM = 7.6 cm. Find:
(a) the area of the parallegram PQRS
(b) QN, if PS = 8 cm
Ans: Given: SR=12 cm, QM = 7.6 cm, PS = 8cm
(a) Area of parallelogram = base x height = 12 x 7.6 = 91.2 cm^{2}
(b) Area of parallelogram = base x height
=> 91.2 = 8 x QN => QN = 91.2/8 = 11.4 cm.
A triangle is a polygon with three vertices, and three sides or edges that are line segments. A triangle with vertices A, B, and C is denoted as ABC.Triangle ABC
To find the area of a triangle within a parallelogram, you can follow these steps
1. Identify the Triangle
2. Understand the Relationship
3. Calculate the Area of the Parallelogram
4. Apply the Relationship for the Triangle
Parallelogram ABCD
All the congruent triangles are equal in area but the triangles equal in area need not be congruent.
Example 1: Find BC, if the area of the triangle ABC is 36 cm^{2} and the height AD is 3 cm.
Ans: Height = 3 cm, Area = 36 cm^{2}
Area of the triangle ABC = 1/2 x b x h
=> 36 = 1/2 x b x 3 => b = 24 cm
Base BC = 24 cm
A circle is defined as a collection of points on a plane that are at an equal distance.
Circle
The distance around a circular region is known as its circumference.
where,
Circumference = Diameter x 3.14
Diameter(d) is equal to twice the radius(r) =2r
Circles with the same centre but different radii are called concentric circles.
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Example: If the radius of the circle is 25 units, find the circumference of the circle. (Take π = 3.14)
Solution: Given, radius = 25 units
Let us write the circumference formula and then we will substitute the value of r (radius) in it.
Circumference of circle formula = 2πr
C = 2 × π × 25
C = 2 × 3.14 × 25 = 157 units
Therefore, the circumference of a circle is 157 units.
The area of a circle is the region enclosed in the circle.
Formulae of area of circle
where
Example 1: The radius of a circular pipe is 10 cm. What length of a tape is required to wrap once around the pipe (π = 3.14)?
Ans: Radius of the pipe (r) = 10 cm
Length of tape required is equal to the circumference of the pipe. Circumference of the pipe = 2πr = 2 × 3.14 × 10 cm = 62.8 cm
Therefore, length of the tape needed to wrap once around the pipe is 62.8 cm.
Example 2: Find the perimeter of the given shape (Take π = 22/7 ).
Ans: In this shape, we need to find the circumference of semicircles on each side of the square.Circumference of the circle = πd
Circumference of the semicircle = 1/2 πd = 1/2 x 22/7 × 14 cm = 22 cm Circumference of each of the semicircles is 22 cm
Therefore, the perimeter of the given figure = 4 × 22 cm = 88 cm.
Example 3: Diameter of a circular garden is 9.8 m. Find its area.
Ans: Diameter, d = 9.8 m
Therefore, radius r = 9.8 ÷ 2 = 4.9 m
Area of the circle = πr^{2} = 22/7 x (4.9)^{2} m^{2} = 22/7 × 4.9 x 4.9 m^{2}= 75.46 m^{2}
Example 4:The adjoining figure shows two circles with the same centre. The radius of the larger circle is 10 cm and the radius of the smaller circle is 4 cm. Find:
(a) the area of the larger circle
(b) the area of the smaller circle
(c) the shaded area between the two circles. (π = 3.14)
Ans:
(a) Radius of the larger circle = 10 cm So, area of the larger circle = πr^{2} = 3.14 × 10 × 10 = 314 cm^{2}
(b) Radius of the smaller circle = 4 cm Area of the smaller circle = πr^{2} = 3.14 × 4 × 4 = 50.24 cm^{2}
(c) Area of the shaded region = (314 – 50.24) cm^{2} = 263.76 cm^{2}
76 videos345 docs39 tests

1. How do you calculate the area of a parallelogram? 
2. What is the formula to find the area of a triangle? 
3. How do you find the circumference of a circle? 
4. How do you calculate the area of a circle? 
5. What is the relationship between the area and perimeter of a shape? 

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