- Perimeter is the total length or total distance covered along the boundary of a closed shape.
- The area is the total amount of surface enclosed by a closed figure.
The perimeter of Square and Rectangle
- Perimeter of a square = a + a + a + a = 4a, where a is the length of each side.
- Perimeter of a rectangle = l + l + b + b = 2(l + b), where l and b are length and breadth, respectively.
Area of Square & Rectangle
Area of square = 4a2
Here a is the length of each side
Area of rectangle = Length(l) × Breadth(b) = l×b
Area of a Parallelogram
- Area of parallelogram ABCD = (base×height)
Area of parallelogram ABCD = (b×h)
Triangle as Part of Rectangle
- The rectangle can be considered as a combination of two congruent triangles.
- Consider a rectangle ABCD, it is divided into 2 triangles ACD and ABD.
- Area of each triangle = 12 (Area of the rectangle).
Area of a Triangle
- Consider a parallelogram ABCD.
- Draw a diagonal BD to divide the parallelogram into two congruent triangles.
- Area of triangle ABD = 1/2 (Area of parallelogram ABCD)
Area of triangle ABD = 1/2 (b×h)
Conversion of Units
- Kilometres, metres, centimetres, millimetres are units of length.
- 10 millimetres = 1 centimetre
- 100 centimetres = 1 metre
- 1000 metres = 1 kilometre
Life of Pi
Terms Related to Circle
- A circle is a simple closed curve which is not a polygon.
- A circle is a collection of points which are equidistant from a fixed point.
- The fixed point in the middle is called the centre.
- The fixed distance is known as radius.
- The perimeter of a circle is also called as the circumference of the circle.
Circumference of a Circle
- The circumference of a circle ( C ) is the total path or total distance covered by the circle. It is also called a perimeter of the circle.
Circumference of a circle = 2×π×r,
where r is the radius of the circle.
Visualizing Area of a Circle
Area of Circle
- Area of a circle is the total region enclosed by the circle.
Area of a circle = π×r2, where r is the radius of the circle.
Introduction and Value of Pi
- Pi (π) is the constant which is defined as the ratio of a circle’s circumference (2πr) to its diameter(2r).
π= Circumference (2πr)/Diameter (2r)
- The value of pi is approximately equal to 3.14159 or 22/7.
Cost of Framing, Fencing
- Cost of framing or fencing a land is calculated by finding its perimeter.
- Example: A square-shaped land has length of its side 10m.
Perimeter of the land = 4 × 10 = 40m
Cost of fencing 1m = Rs 10
Cost of fencing the land = 40 m × Rs 10 = Rs 400
Cost of Painting, Laminating
- Cost of painting a surface depends on the area of the surface.
- Example: A wall has dimensions 5m×4m.
Area of the wall = 5m×4m=20m2
Cost of painting 1m2 of area is Rs 20.
Cost of painting the wall =20m2×Rs 20=Rs 400
Area of Mixed Shapes
- Find the area of the shaded portion using the given information.
Solution: Diameter of the semicircle = 10cm
Radius of semicircle = 5cm
Area of the shaded portion = Area of rectangle ABCD – Area of semicircle
Area of the shaded portion = (l×b) − (πr2/2)
= 30×10 − (π×52/2)
= 300 − (π×25/2)
= (600 – 25π)/2
= (600 – 78.5)/2
= 260.7 cm2