Area of Plane Figures and Surface Area from "summary" of NCERT Class 10 Mathematics Solutions by JagranJosh
Area of plane figures refers to the measurement of the region covered by a two-dimensional shape. It is expressed in square units and helps us determine how much space is enclosed within the boundaries of the shape. The concept of area is essential in various fields such as construction, architecture, geometry, and more. By calculating the area of a shape, we can understand its size and make informed decisions based on the available space. Surface area, on the other hand, pertains to the total area occupied by the surface of a three-dimensional object. It includes the area of all the faces or surfaces of the object. Surface area is crucial in real-life scenarios like packaging materials, painting walls, designing objects, and so on. Understanding the surface area of an object helps us estimate the amount of material required for covering or painting it, leading to cost-effective solutions. Calculating the area of plane figures involves applying specific formulas based on the shape of the figure. For example, the area of a rectangle is determined by multiplying its length and width. Similarly, the area of a circle is calculated using the formula πr², where 'r' represents the radius of the circle. By knowing the formulas for different shapes, we can accurately find the area of any given figure. To find the surface area of three-dimensional objects like cubes, cuboids, cylinders, cones, and spheres, we need to use appropriate formulas for each shape. For instance, the surface area of a cube is obtained by multiplying the area of one face by the total number of faces. On the other hand, the surface area of a cylinder is calculated by adding the areas of its two circular bases and the lateral surface area. Understanding the concepts of area of plane figures and surface area is crucial for solving mathematical problems and practical applications. By mastering these concepts, we can make informed decisions, plan effectively, and optimize resources in various situations. Moreover, these concepts play a vital role in developing problem-solving skills, logical reasoning, and spatial visualization abilities, making them essential aspects of mathematics education.
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