MENSURATION 2D
Mensuration is a mathematical branch that involves the computation of dimensions such as length, width, height, area, volume, and similar attributes. It is categorized into three primary components: Volume, Area, and Perimeter. Mensuration refers to a segment of mathematics dedicated to quantifying the length, volume, or area of diverse geometric forms, which can manifest in either two or three dimensions
What is Mensuration 2D?
Mensuration in the context of geometry refers to the branch of mathematics that deals with the measurement of geometric figures and their properties. In 2D (two-dimensional) mensuration, the focus is on measuring and calculating the characteristics of flat, planar shapes. Common 2D geometric figures include squares, rectangles, triangles, circles, and polygons.
Here are some key concepts and formulas related to 2D mensuration for some basic geometric shapes:
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Mensuration 2D Formulas
| Shape | Perimeter | Area |
|---|---|---|
| Square | 4s | s² |
| Rectangle | 2(l + w) | l × w |
| Triangle | a + b + c | ½ * b * h |
| Right Triangle | a + b + c | ½ * b * h (where b and h are legs) |
| Equilateral Triangle | 3s | √3 / 4 * s² |
| Isosceles Triangle | 2(a + b) | ½ * b * h (where b is the base) |
| Scalene Triangle | a + b + c | K = √(s - a)(s - b)(s - c), A = √K / 4 |
| Parallelogram | 2(l + b) | b × h |
| Rhombus | 4d | ½ * d1 * d2 |
| Trapezium | a + b + c + d | ½ * h * (a + d) |
| Circle | 2πr | πr² |
| Sector (of a circle) | θ/360 * 2πr | (θ/360) * πr² |
Formulas for Mensuration 2D Shapes
| Shape | Perimeter | Area | Additional Measures |
|---|---|---|---|
| Square | 4s | s² | Diagonals: d = √2s |
| Rectangle | 2(l + w) | l × w | Diagonals: d² = l² + w² |
| Triangle | a + b + c | ½ * b * h | Types: Equilateral, Isosceles, Scalene |
| Right Triangle | a + b + c | ½ * b * h (where b and h are legs) | Hypotenuse: c² = a² + b² |
| Equilateral Triangle | 3s | √3 / 4 * s² | |
| Isosceles Triangle | 2(a + b) | ½ * b * h (where b is the base) | Base angles: (180° - θ) / 2 |
| Scalene Triangle | a + b + c | K = √(s - a)(s - b)(s - c), A = √K / 4 | Semi-perimeter (s): s = (a + b + c) / 2 |
| Parallelogram | 2(l + b) | b × h | Base = b, height = h |
| Rhombus | 4d | ½ * d1 * d2 | Diagonals perpendicular, d1² + d2² = 4a² |
| Trapezium | a + b + c + d | ½ * h * (a + d) | Bases = a and d, height = h |
| Circle | 2πr | πr² | Circumference = 2πr, radius = r |
| Sector (of a circle) | θ/360 * 2πr | (θ/360) * πr² | Central angle = θ, radius = r |
| Kite | a + b + c + d | (√(a² + d²) + √(b² + c²)) / 2 | Diagonals intersect at right angles, diagonals = a and d |
Difference Between Mensuration 2D and 3D Shapes
| Feature | Mensuration 2D Shapes | Mensuration 3D Shapes |
|---|---|---|
| Dimensions | 2 dimensions (length, width/breadth) | 3 dimensions (length, width/breadth, height/depth) |
| Shapes | Flat, no depth or thickness | Solid, occupy space in all directions |
| Visualization | Can be drawn on a flat surface | Require multiple views or drawings for complete representation |
| Measurements | Perimeter and Area | Volume, Surface Area (lateral, total), and sometimes curved surface area |
| Formulas | Relatively simple and straightforward | More complex, often involving multiplication and additional variables |
| Applications | Real-world examples: floor plans, fabric calculations, map scales | Real-world examples: containers, building volumes, object dimensions |
| Challenges | Mainly involve calculations with basic geometric equations | Require understanding of spatial relationships and visualizing shapes in 3D |
| Mathematical concepts | Primarily focused on basic geometry | May involve concepts like prisms, pyramids, spheres, and cylinders |
Solved Examples of Mensuration 2D
Solution:
Answer: The perimeter is 24 cm, and the area is 36 cm²
Solution:
Answer: The perimeter is 26 meters, and the area is 40 square meters |
