Mensuration 2D with Area and Perimeter Examples
Mensuration 2D deals with the measurement of plane figures such as squares, rectangles, triangles, circles, parallelograms, rhombuses and trapeziums. The main quantities are perimeter, circumference and area. This page covers mensuration 2D formulas, properties, unit conversions, composite figures and direct calculation methods used in quantitative aptitude.
What is Mensuration 2D?
Perimeter and circumference are expressed in linear units such as cm or m. Area is expressed in square units such as cm² or m². For a figure made of several non-overlapping parts, calculate the required areas separately and add or subtract them according to the figure. For example, a rectangle of length 8 cm and breadth 5 cm has perimeter 2(8 + 5) = 26 cm and area 8 × 5 = 40 cm².
Mensuration 2D Video Lessons
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Area of Combined Shapes
Learn how to calculate the area of complex figures by dividing them into simpler geometric shapes and combining their individual areas accurately.
Mensuration 2D Formula & Tricks
Important Formulas
Here, a is the side of the square.
Here, l is the length and b is the breadth.
The height must be perpendicular to the chosen base.
All three sides have length a.
The height is measured perpendicular to the selected base.
The diagonals d₁ and d₂ are used for the area.
a and b are the parallel sides and h is the perpendicular distance between them.
r is the radius. Use π = 22/7 or 3.14 as specified.
Quick Tricks
Convert all lengths to one unit before applying a formula. If a length is converted from metres to centimetres, its area conversion is obtained by squaring the factor.
Divide an irregular figure into familiar rectangles, triangles, circles or semicircles. Add the areas of parts inside the figure and subtract any missing parts.
Since d = 2r, circumference can be written as πd and circle area can be written as πd²/4.
For a uniform path around a figure, calculate the outer area and subtract the inner area. For a circular path, use π(R² − r²).
Mensuration 2D Concepts
Perimeter and Area of Basic Figures
For a square, perimeter is 4a and area is a². For a rectangle, perimeter is 2(l + b) and area is lb. For a triangle, perimeter is a + b + c and area is 1/2 × base × perpendicular height.
Circle, Semicircle and Quadrant
For a semicircle, area is 1/2πr². Its curved boundary is πr, while its complete perimeter including the diameter is πr + 2r. A quadrant has area 1/4πr² and arc length 1/2πr.
Parallelogram, Rhombus and Trapezium
Opposite sides of a parallelogram are equal. A rhombus has all sides equal, but its diagonals need not be equal. In a trapezium, a and b are the parallel sides, and h is the perpendicular distance between them.
Composite Figures and Paths
For a rectangular path around a rectangle, path area = outer rectangle area − inner rectangle area. For a circular ring, path area = π(R² − r²), where R is the outer radius and r is the inner radius. Boundary lengths must include only the edges requested in the question.
Unit Conversion in Mensuration
Since 1 m = 100 cm, 1 m² = 100² cm² = 10,000 cm². Similarly, 1 km² = 1,000,000 m². Keep perimeter in linear units and area in square units.
Mensuration 2D Visual Guide & Data
Use the table and chart below to understand the data better.
Mensuration 2D Formula Summary
Common perimeter, circumference and area formulas for plane figures.
| Figure | Perimeter or Circumference | Area |
|---|---|---|
| Square | 4a | a² |
| Rectangle | 2(l + b) | lb |
| Triangle | a + b + c | 1/2 × base × height |
| Parallelogram | 2(a + b) | base × height |
| Rhombus | 4a | 1/2 × d₁ × d₂ |
| Circle | 2πr | πr² |
Note: Use consistent units for all dimensions. In the rhombus formula, d₁ and d₂ are the diagonals.
Rectangle with Length and Breadth
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Mensuration 2D Revision Points
Key formulas and rules for quick revision.
- Perimeter measures boundary length; area measures enclosed surface.
- Rectangle: perimeter = 2(l + b), area = lb.
- Square: perimeter = 4a, area = a².
- Triangle: area = 1/2 × base × perpendicular height.
- Circle: circumference = 2πr, area = πr².
- Semicircle perimeter including diameter = πr + 2r.
- Trapezium area = 1/2 × sum of parallel sides × height.
- Rhombus area = 1/2 × product of diagonals.
Mensuration 2D FAQs
What is the formula for the area of a rectangle?
Area = length × breadth. For a rectangle measuring 9 cm by 4 cm, the area is 9 × 4 = 36 cm².
What is the difference between the perimeter and area of a circle?
The circumference measures the boundary and equals 2πr. The area measures the enclosed region and equals πr².
What is the complete perimeter of a semicircle?
Complete perimeter = curved part + diameter = πr + 2r. The curved part alone is πr.
How is the area of a trapezium calculated?
Area = 1/2 × (sum of parallel sides) × perpendicular height. If the parallel sides are 8 cm and 12 cm and height is 5 cm, area = 1/2 × 20 × 5 = 50 cm².
How do you find the side of a square when its area is known?
Side = √area. If the area is 144 cm², the side is √144 = 12 cm.
What is the area of a circular path?
For outer radius R and inner radius r, area of the path = π(R² − r²). For R = 7 cm and r = 5 cm, it is 24π cm².