{"id":34753,"date":"2023-01-10T14:11:58","date_gmt":"2023-01-10T08:41:58","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=34753"},"modified":"2023-01-11T09:23:55","modified_gmt":"2023-01-11T03:53:55","slug":"mensuration","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/mensuration\/","title":{"rendered":"Mensuration &#8211; Definition, Introduction, Formulas, Solved Problems"},"content":{"rendered":"<p>In Maths Mensuration is nothing but a measurement of 2-D and 3-D Geometrical Figures. Mensuration is the study of the measurement of shapes and figures. We can measure the area, perimeter, and volume of geometrical shapes such as Cube, Cylinder, Cone, Cuboid, Sphere, and so on.<\/p>\n<p>Keep reading this page to learn deeply about the mensuration. We can solve the problems easily, if and only we know the formulas of the particular shape or figure. This article helps to learn the mensuration formulae with examples. Learn the difference between the 2-D and 3-D shapes from here. Understand the concept of Mensuration by using various formulas.<\/p>\n<ul>\n<li><a href=\"https:\/\/ccssanswers.com\/area-and-perimeter\/\">Area and Perimeter<\/a><\/li>\n<li><a href=\"https:\/\/ccssanswers.com\/perimeter-and-area-of-rectangle\/\">Perimeter and Area of Rectangle<\/a><\/li>\n<li><a href=\"https:\/\/ccssanswers.com\/perimeter-and-area-of-square\/\">Perimeter and Area of Square<\/a><\/li>\n<li><a href=\"https:\/\/ccssanswers.com\/area-of-the-path\/\">Area of the Path<\/a><\/li>\n<li><a href=\"https:\/\/ccssanswers.com\/area-and-perimeter-of-the-triangle\/\">Area and Perimeter of the Triangle<\/a><\/li>\n<li><a href=\"https:\/\/ccssanswers.com\/area-of-parallelogram\/\">Area of Parallelogram<\/a><\/li>\n<li><a href=\"https:\/\/ccssanswers.com\/area-of-rhombus-formula\/\">Area of Rhombus<\/a><\/li>\n<li><a href=\"https:\/\/ccssanswers.com\/area-of-trapezium\/\">Area of Trapezium<\/a><\/li>\n<li><a href=\"https:\/\/ccssanswers.com\/circumference-and-area-of-circle\/\">Circumference and Area of Circle<\/a><\/li>\n<li><a href=\"https:\/\/ccssanswers.com\/area-conversion\/\">Area Conversion<\/a><\/li>\n<li><a href=\"https:\/\/ccssanswers.com\/practice-test-on-area-and-perimeter-of-rectangle\/\">Practice Test on Area and Perimeter of Rectangle<\/a><\/li>\n<li><a href=\"https:\/\/ccssanswers.com\/practice-test-on-area-and-perimeter-of-square\/\">Practice Test on Area and Perimeter of Square<\/a><\/li>\n<\/ul>\n<h2>Definition of Mensuration<\/h2>\n<p>Mensuration is the theory of measurement. It is the branch of mathematics that is used for the measurement of various figures like the cube, cuboid, square, rectangle, cylinder, etc. We can measure the 2 Dimensional and 3 Dimensional figures in the form of Area, Perimeter, Surface Area, Volume, etc.<\/p>\n<h3>What is a 2-D Shape?<\/h3>\n<p>The shape or figure with two dimensions like length and width is known as the 2-D shape. An example of a 2-D figure is a Square, Rectangle, Triangle, Parallelogram, Trapezium, Rhombus, etc. We can measure the 2-D shapes in the form of Area (A) and Perimeter (P).<\/p>\n<h3>What is 3-D Shape?<\/h3>\n<p>The shape with more or than two dimensions such as length, width, and height then it is known as 3-D figures. Examples of 3-Dimensional figures are Cube, Cuboid, Sphere, Cylinder, Cone, etc. The 3D figure is determined in the form of Total Surface Area (TSA), Lateral Surface Area (LSA), Curved Surface Area (CSA), and Volume (V).<\/p>\n<h3>Introduction to Mensuration<\/h3>\n<p>The important terminologies that are used in mensuration are Area, Perimeter, Volume, TSA, CSA, LSA.<\/p>\n<ul>\n<li><strong>Area:<\/strong> The Area is an extent of two-dimensional figures that measure the space occupied by the closed figure. The units for Area is square units. The abbreviation for Area is A.<\/li>\n<li><strong>Perimeter:<\/strong> The perimeter is used to measure the boundary of the closed planar figure. The units for Perimeter is cm or m. The abbreviation for Perimeter is P.<\/li>\n<li><strong>Total Surface Area:<\/strong> The total surface area is the combination or sum of both lateral surface area and curved surface area. The units for the total surface area is square cm or m. The abbreviation for the total surface area is TSA.<\/li>\n<li><strong>Lateral Surface Area:<\/strong> It is the measure of all sides of the object excluding top and base. The units for the lateral surface area is square cm or m. The abbreviation for the lateral surface area is LSA.<\/li>\n<li><strong>Curved Surface Area:<\/strong> The area of a curved surface is called a Curved Surface Area. The units of the curved surface area are square cm or m. The abbreviation for the curved surface area is CSA.<\/li>\n<li><strong>Volume:<\/strong> Volume is the measure of the three dimensional closed surfaces. The units for volume is cubic cm or m. The abbreviation for Volume is V.<\/li>\n<\/ul>\n<h3>Mensuration Formulas for 2-D Figures<\/h3>\n<p>Check out the formulas of 2-dimensional figures from here. By using these mensuration formulae students can easily solve the problems of 2D figures.<\/p>\n<p><strong>1. Rectangle:<\/strong><\/p>\n<ul>\n<li>Area = length \u00d7 width<\/li>\n<li>Perimeter = 2(l + w)<\/li>\n<\/ul>\n<p><strong>2. Square:<\/strong><\/p>\n<ul>\n<li>Area = side \u00d7 side<\/li>\n<li>Perimeter = 4 \u00d7 side<\/li>\n<\/ul>\n<p><strong>3. Circle:<\/strong><\/p>\n<ul>\n<li>Area = \u03a0r\u00b2<\/li>\n<li>Circumference = 2\u03a0r<\/li>\n<li>Diameter = 2r<\/li>\n<\/ul>\n<p><strong>4. Triangle:<\/strong><\/p>\n<ul>\n<li>Area = 1\/2 \u00d7 base \u00d7 height<\/li>\n<li>Perimeter = a + b + c<\/li>\n<\/ul>\n<p><strong>5. Isosceles Triangle:<\/strong><\/p>\n<ul>\n<li>Area = 1\/2 \u00d7 base \u00d7 height<\/li>\n<li>Perimeter = 2 \u00d7 (a + b)<\/li>\n<\/ul>\n<p><strong>6. Scalene Triangle:<\/strong><\/p>\n<ul>\n<li>Area = 1\/2 \u00d7 base \u00d7 height<\/li>\n<li>Perimeter = a + b + c<\/li>\n<\/ul>\n<p><strong>7. Right Angled Triangle:<\/strong><\/p>\n<ul>\n<li>Area =\u00a01\/2 \u00d7 base \u00d7 height<\/li>\n<li>Perimeter = b + h + hypotenuse<\/li>\n<li>Hypotenuse c = a\u00b2+b\u00b2<\/li>\n<\/ul>\n<p><strong>8. Parallelogram:<\/strong><\/p>\n<ul>\n<li>Area = a \u00d7 b<\/li>\n<li>Perimeter = 2(l + b)<\/li>\n<\/ul>\n<p><strong>9. Rhombus:<\/strong><\/p>\n<ul>\n<li>Area = 1\/2 \u00d7 d1 \u00d7 d2<\/li>\n<li>Perimeter = 4 \u00d7 side<\/li>\n<\/ul>\n<p><strong>10. Trapezium:<\/strong><\/p>\n<ul>\n<li>Area = 1\/2 \u00d7 h(a + b)<\/li>\n<li>Perimeter = a + b + c + d<\/li>\n<\/ul>\n<p><strong>11. Equilateral Triangle:<\/strong><\/p>\n<ul>\n<li>Area = \u221a3\/4 \u00d7 a\u00b2<\/li>\n<li>Perimeter = 3a<\/li>\n<\/ul>\n<h3>Mensuration Formulas of 3D Figures<\/h3>\n<p>The list of the mensuration formulae for 3-dimensional shapes is given below. Learn the relationship between the various parameters from here.<\/p>\n<p><strong>1. Cube:<\/strong><\/p>\n<ul>\n<li>Lateral Surface Area = 4a\u00b2<\/li>\n<li>Total Surface Area = 6a\u00b2<\/li>\n<li>Volume = a\u00b3<\/li>\n<\/ul>\n<p><strong>2. Cuboid:<\/strong><\/p>\n<ul>\n<li>Lateral Surface Area = 2h(l + b)<\/li>\n<li>Total Surface Area = 2(lb + bh + lh)<\/li>\n<li>Volume = length \u00d7 breadth \u00d7 height<\/li>\n<\/ul>\n<p><strong>3. Cylinder:<\/strong><\/p>\n<ul>\n<li>Lateral Surface Area = 2\u03a0rh<\/li>\n<li>Total Surface Area = 2\u03a0rh + 2\u03a0r\u00b2<\/li>\n<li>Volume = \u03a0r\u00b2h<\/li>\n<\/ul>\n<p><strong>4. Cone:<\/strong><\/p>\n<ul>\n<li>Lateral Surface Area = \u03a0rl<\/li>\n<li>Total Surface Area = \u03a0r(r + l)<\/li>\n<li>Volume = 1\/3\u00a0\u03a0r\u00b2h<\/li>\n<\/ul>\n<p><strong>5. Sphere:<\/strong><\/p>\n<ul>\n<li>Lateral Surface Area = 4\u03a0r\u00b2<\/li>\n<li>Total Surface Area =\u00a04\u03a0r\u00b2<\/li>\n<li>Volume =\u00a0(4\/3)\u03a0r\u00b3<\/li>\n<\/ul>\n<p><strong>6. Hemisphere:<\/strong><\/p>\n<ul>\n<li>Lateral Surface Area = 2\u03a0r\u00b2<\/li>\n<li>Total Surface Area = 3\u03a0r\u00b2<\/li>\n<li>Volume = (2\/3)\u03a0r\u00b3<\/li>\n<\/ul>\n<h3>Solved Problems on Mensuration<\/h3>\n<p>Here are some questions that help you to understand the concept of Mensuration. Use the Mensuration formulas to solve the problems.<\/p>\n<p><strong>1. Find the Length of the Rectangle whose Perimeter is 24 cm and Width is 3 cm?<\/strong><\/p>\n<p>Solution:<\/p>\n<p>Given that,<br \/>\nPerimeter = 24 cm<br \/>\nWidth = 3 cm<br \/>\nPerimeter of the rectangle = 2(l + w)<br \/>\n24 cm = 2(l + 3 cm)<br \/>\n2l + 6 = 24<br \/>\n2l + 6 = 24<br \/>\n2l = 24 &#8211; 6 = 18<br \/>\n2l = 18<br \/>\nl = 9 cm<br \/>\nThus length of the rectangle = 9 cm<\/p>\n<p><strong>2. Calculate the volume of the Cuboid whole base area is 60 cm\u00b2 and height is 5 cm.<\/strong><\/p>\n<p>Solution:<\/p>\n<p>Given,<br \/>\nBase area = 60 cm\u00b2<br \/>\nHeight = 5 cm<br \/>\nVolume of the Cuboid = base area \u00d7 height<br \/>\nV = 60 cm\u00b2 \u00d7 5 cm<br \/>\nV = 300 cm\u00b3<br \/>\nThus the volume of the cuboid is 300 cm\u00b3.<\/p>\n<p><strong>3. Find the area of the Cube whose side is 10 centimeters.<\/strong><\/p>\n<p>Solution:<\/p>\n<p>Given, side = 10 cm<br \/>\nLateral Surface Area = 4a\u00b2<br \/>\nLSA = 4 \u00d7 10 \u00d7 10 = 400 cm\u00b2<br \/>\nTotal Surface Area = 6a\u00b2<br \/>\n= 6 \u00d7 10 \u00d7 10 = 600 cm\u00b2<br \/>\nVolume of the cube = a\u00b3<br \/>\nV = 10 \u00d7 10 \u00d7 10 = 1000 cm\u00b3<br \/>\nTherefore the volume of the cube is 1000 cubic centimeters.<\/p>\n<p><strong>4. What is the lateral surface area of the sphere if the radius is 5 cm.<\/strong><\/p>\n<p>Solution:<\/p>\n<p>Given,<br \/>\nThe radius of the sphere = 5 cm<br \/>\nThe formula for LSA of sphere = 4\u03a0r\u00b2<br \/>\n\u03a0 = 3.14 or 22\/7<br \/>\nLSA = 4 \u00d7 3.14 \u00d7 5 cm \u00d7 5 cm<br \/>\nLSA = 314 sq. cm<br \/>\nThus the lateral surface area of the sphere is 314 sq. cm<\/p>\n<p><strong>5. What is the area of the parallelogram if the base is 15 cm and height is 10 cm.<\/strong><\/p>\n<p>Solution:<\/p>\n<p>Given, Base = 15 cm<br \/>\nHeight = 10 cm<br \/>\nWe know that,<br \/>\nArea of parallelogram = bh<br \/>\nA = 15 cm \u00d7 10 cm<br \/>\nA = 150 sq. cm<br \/>\nTherefore the area of the parallelogram is 150 sq. cm.<\/p>\n<h3>FAQs on Mensuration<\/h3>\n<p><strong>1. What is the use of Mensuration?<\/strong><\/p>\n<p>Mensuration is used to find the length, area, perimeter, and volume of the geometric figures.<\/p>\n<p><strong>2. What is the difference between 2D and 3D figures?<\/strong><\/p>\n<p>In 2D we can measure the area and perimeter. In 3D we can measure LSA, TSA, and Volume.<\/p>\n<p><strong>3. What is Mensuration in Math?<\/strong><\/p>\n<p>Mensuration is the branch of mathematics that studies the theory of measurement of 2D and 3D geometric figures or shapes.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In Maths Mensuration is nothing but a measurement of 2-D and 3-D Geometrical Figures. Mensuration is the study of the measurement of shapes and figures. We can measure the area, perimeter, and volume of geometrical shapes such as Cube, Cylinder, Cone, Cuboid, Sphere, and so on. 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