Table of contents  
Area of Parallelograms  
Area of Triangle  
Circles  
Circumference of Circle  
Area of Circle 
A picture of a garden is given below. You have to cover the boundaries with flowers.
How would you calculate the measurement of the boundaries of the garden?
To find the distance around the boundaries of the garden, you need to calculate the perimeter. To find the perimeter of this rectangle, we add up all the sides.
So we add 16.3m + 16.7m + 16.3m + 16.7m, which is equal to 66m. So, the perimeter of the rectangle is equal to 66m.
Now, if we have to cover the whole garden, how would you calculate the space inside the garden?
To calculate this, we will need to find the area of the garden.
The area is the amount of space inside a shape. For a rectangle, we find the area by multiplying the length by the width.
So area is equal to 16.3m x 16.7m, which is equal to 272.21m^{2}.
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:
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
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 2: 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, you can follow these steps
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 cm2 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
Diameter: Any straight line segment that passes through the centre of a circle and whose end points are on the circle is called its diameter.
Radius: Any line segment from the centre of the circle to its circumference.
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.
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. What is the formula to calculate the area of a parallelogram? 
2. How do you find the area of a triangle? 
3. What is the formula to find the circumference of a circle? 
4. How can you calculate the area of a circle? 
5. How do you find the area of a parallelogram if the base and height are given? 

Explore Courses for Class 7 exam
