Perimeter is the total length of the boundary of a closed figure. Area is the measure of the region enclosed by the boundary. Both are important for solving practical problems in real life.
- Squares and Rectangles:
- Perimeter of square = 4 x side = 4s
- Area of square = side x side = s2
- Perimeter of rectangle = 2 x (length + breadth) = 2(l + b)
- Area of rectangle = length x breadth = l x b
- Triangles:
- Area of triangle = (1/2) x base x height
Parallelograms:
A parallelogram has two pairs of parallel sides. Its area is calculated as:
- Area of parallelogram = base x height
Note: The height is the perpendicular distance between the parallel sides (NOT the slant side).
- Circles:
- Circumference (perimeter) of circle = 2 x pi x r = 2pi r
- Area of circle = pi x r2
- Where r is the radius and pi is approximately 22/7 or 3.14.
Conversion of Units:
1 m = 100 cm, 1 m2 = 10000 cm2
1 km = 1000 m, 1 km2 = 1000000 m2
1 hectare = 10000 m2
Find the area of a rectangle with length 8 cm and breadth 5 cm.
Area = 8 x 5 = 40 sq cm.
The perimeter of a square is 48 cm. Find its area.
Side = 48/4 = 12 cm. Area = 12 x 12 = 144 sq cm.
Find the area of a triangle with base 10 cm and height 7 cm.
Area = (1/2) x 10 x 7 = 35 sq cm.
A parallelogram has base 12 cm and height 8 cm. Find its area.
Area = 12 x 8 = 96 sq cm.
Find the circumference and area of a circle with radius 14 cm. (Use pi = 22/7)
Circumference = 2 x (22/7) x 14 = 88 cm.
Area = (22/7) x 14 x 14 = 22 x 2 x 14 = 616 sq cm.
A room is 5 m long and 4 m wide. What is the cost of tiling it at Rs 200 per sq m?
Area = 5 x 4 = 20 sq m. Cost = 20 x 200 = Rs 4000.
Find the area of a figure that is a rectangle (6 cm x 4 cm) with a triangular notch (base 2 cm, height 4 cm) removed from one side.
Area of rectangle = 24 sq cm. Area of triangle = (1/2) x 2 x 4 = 4 sq cm. Remaining area = 24 - 4 = 20 sq cm.
- Key Formulas:
- Rectangle: P = 2(l+b), A = lb
- Square: P = 4s, A = s2
- Triangle: A = (1/2) x b x h
- Parallelogram: A = b x h
- Circle: C = 2pi r, A = pi r2
Common mistakes
Do not confuse the height of a parallelogram (which is perpendicular to the base) with the slant side. For circles, double-check whether the question asks for area (pi r2) or circumference (2 pi r).
Summary
Perimeter is the boundary length; area is the enclosed region. Different shapes have different formulas. Area of composite figures is found by adding or subtracting areas of simpler shapes. Unit conversions are essential when solving practical problems.