Mensuration Calculator | Plane Figure (2D)

Mensuration is an essential branch of mathematics that deals with measuring geometric shapes and their properties. It is used to calculate areas, perimeters, and volumes of various geometrical figures, making it an indispensable part of everyday calculations and academic studies. This article focuses on the mensuration of 2D plane figures and introduces our Mensuration Calculator, which offers step-by-step solutions for free use. Whether you are a student or a professional, understanding mensuration concepts will help you tackle problems efficiently.

What is Mensuration?

Mensuration is the branch of geometry that deals with the measurement of various parameters of geometrical shapes, such as:

• Perimeter: The total length of the boundary of a figure.

• Area: The surface enclosed within the figure's boundaries.

In this article, we focus on 2D Plane Figures, which include shapes like squares, rectangles, circles, triangles, and more. These are called plane figures because they exist in a two-dimensional plane, having only length and breadth.

Key Terms in Mensuration

1. Perimeter:

   • The sum of the lengths of all sides of a plane figure.

   • Example: The perimeter of a square is given by l + l + l + l = 4l.

2. Area:

   • The space enclosed within a shape.

   • Example: The area of a rectangle is length × breadth.

3. Mensuration Formulae:

   • Each plane figure has specific formulas for calculating its area and perimeter.

4. Mensuration 2D:

   • Focuses exclusively on two-dimensional shapes such as squares, rectangles, triangles, circles, and parallelograms.

Common Plane Figures and Their Properties

1. Square

• Properties:

  • All sides are equal.

  • All angles are 90^o.

• Perimeter = 4l

• Area = l²

2. Rectangle

• Properties:

  • Opposite sides are equal and parallel.

  • All angles are 90^o.

• Perimeter = 2(l + b)

• Area = l × b

3. Circle

• Properties:

  • A set of points equidistant from a central point.

• Circumference = 2𝜋r

• Area = 𝜋r²

4. Triangle

• Properties:

  • Three sides and three angles.

  • The sum of all angles is 180^o.

• Perimeter: Sum of all sides = a + b + c

• Area (Heron’s formula): 

  Area = √[s(s - a)(s - b)(s - c)]

  where:

  • a, b, and c are the lengths of the three sides of the triangle.
  • s is the semiperimeter of the triangle, calculated as: s = (a + b + c) / 2

5. Parallelogram

• Properties:

  • Opposite sides are equal and parallel.

  • Opposite angles are equal.

• Perimeter = 2(l +b)

• Area = base × height

How to Solve Mensuration Problems

Example 1: Finding the Perimeter of a Rectangle

• Given:

  • Length (l) = 10 cm

  • Breadth (b) = 5 cm

• Solution: Perimeter = 2(l + b) = 2 (10 + 5) = 2 × 15 = 30 cm

Example 2: Calculating the Area of a Circle

• Given:

  • Radius (r) = 7 cm

• Solution: Area = 𝜋r² = 22/7 × 7 = 22 cm²

Example 3: Area of a Triangle (Using Heron’s Formula)

• Given:

  • Sides: a = 7 cm, b = 8 cm, c = 9 cm

• Solution:

  1. Calculate semi-perimeter:

  2. Use Heron’s formula:

     Substituting values:

     s = (a + b + c) / 2 = 7+8+9/2 = 12

     Area = √[s(s - a)(s - b)(s - c)]

     = √[12(12 - 7)(12 - 8)(12 - 9)]

     = √720

     = 26.8 cm²

The Mensuration Calculator

To make solving mensuration problems easier, we present our Mensuration Calculator. This tool is designed to handle various 2D mensuration problems with precision and speed, offering detailed, step-by-step solutions for free.

Features of the Mensuration Calculator

1. User-Friendly Interface:

   • Input values easily and get results instantly.

2. Step-by-Step Solutions:

   • Understand the calculations behind every solution.

3. Versatility:

   • Covers a wide range of shapes, including squares, rectangles, circles, triangles, and more.

4. Free to Use:

   • Accessible to students, teachers, and anyone needing quick solutions.

Example Problems Using the Mensuration Calculator

Example 1: Finding the Perimeter of a Square

• Given: Side (l) = 6 cm

• Solution Using Calculator:

  • Enter

  • Output: l = 6cm

Example 2: Solving for the Area of a Parallelogram

• Given:

  • Base (b) = 8 cm

  • Height (h) = 5 cm

• Solution Using Calculator:

  • Enter b = 8 cm and h = 5 cm

  • Output: Area = b × h = 8 × 5 = 40 cm²

Example 3: Finding the Area of a Circle

• Given:

  • Radius (r) = 10 cm

• Solution Using Calculator:

  • Enter r = 10 cm

  • Output: Area = 𝜋r² = 3.14 × 10 = 31.4 cm²

Applications of Mensuration in Real Life

1. Architecture and Construction:

   • Used for calculating materials, areas, and costs.

2. Agriculture:

   • Helps determine the size of plots and the area for planting.

3. Design and Manufacturing:

   • Essential for creating products with precise measurements.

4. Education:

   • Forms a core part of school-level math curriculums, such as class 7 mensuration.

5. Physics and Engineering:

   • Used to calculate cross-sections, fluid dynamics, and more.

Why Choose Our Mensuration Calculator?

1. Accuracy:

   • Delivers precise results with detailed explanations.

2. Convenience:

   • Saves time and effort in manual calculations.

3. Educational Value:

   • Helps students grasp concepts effectively.

4. Free Access:

   • Available to all users without restrictions.

Conclusion

Mensuration is a vital part of mathematics with extensive applications in daily life and academic learning. Mastering the formulas and solving problems related to mensuration 2D will not only improve your mathematical skills but also enhance your problem-solving abilities. Our Mensuration Calculator makes this process seamless by providing accurate, step-by-step solutions for free. Whether you are calculating the area of a triangle, finding the perimeter of a rectangle, or solving complex geometry problems, our tool is here to help. Start using the Mensuration Calculator today and make math easier and more engaging!