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RS Aggarwal Class 10 Chapter 15 Solutions (Perimeter and Area of Plane Figures)

RS Aggarwal Solutions for Class 10 Maths Chapter 15 is an ideal book to follow for learning the different concepts around perimeter and areas of plane figures. In this chapter of RS Aggarwal Class 10 Maths Solutions, you get to learn how to calculate the perimeter and areas of plane figures and many important formulas related to that. The exercise questions also involve a combination of plane figures such as circle, semicircle, triangle, rectangle, etc. There are interesting questions like finding the area of a park whose length or perimeter is given, or cost of painting a wall is given and you need to find its area or perimeter.

This chapter has a total of 77 questions spread into 3 sections of short and long answer types as well as objective type questions. Many of the questions are based on real-life problems which will enhance your creative abilities. All the exercise questions of the chapter are based on the latest CBSE Class 10 Maths syllabus for board exams. Practising them will certainly help in enhancing your performance in the exams. 

You would be amazed how easy it would be for you to solve any mathematical problem related to perimeter and areas of plane figures if you follow our solutions for this chapter. We have a team of experts who have done extensive research on how to make it easy for you to tackle any mathematical problem and score good marks in Class 10 board exams. Our solutions are free to access whenever required. 

Important Topics for RS Aggarwal Solutions for Class 10 Chapter 15: Perimeter and Areas of Plane Figures

The concept of area and perimeter is used widely in real-life scenarios like fencing of a plot, cost needed to build a house, etc. Let us take a look at some of the definitions and formulas of common plane figures.

  • Perimeter – We use Perimeter to measure the boundaries, the total length of the boundary is the perimeter of the given plane figure. It has the same unit as that of length which is meter, centimetre, millimetre, etc.
  • Area of a plane figure – Area of a plane figure like a circle or triangle is defined by the region of the plane that the figure’s boundary encloses within it. Its unit is in square lengths like cm2 (centimetre square) or m2 (meter square).
  • Perimeter and areas of some plane figures:
    • Rectangle – If l is the length and b is the breadth of a rectangular figure then:
      •    Area = l * b
      •    Perimeter = (2 * l) + (2 * b)
      •   Diagonal = √l2 +b2
    • Square – Square has equal length sides, so if l is the length of its side then:
      •      Area = l * l
      •      Perimeter = 4 * l
      •      Diagonal = l√2
    • Triangle – If a, b, and h are the length of the sides of a triangle where b is its base and h is its height then:
      •      Perimeter = a + b + h
      •      Area = √p2(p2– a) (p2– b) (p2– h) = ½*b*h,  where p2= perimeter/2

     For an equilateral triangle with all sides equal, 

      •     Area = (x2*√3)/4, here x is the side of the triangle        
    • Circle – If r is the radius of the circle and d its diameter then:
      •     Area = πr2
      •     Circumference of circle = 2πr = πd
      •     You could find the area of a ring with the formula = Area of the outer circle – Area of the inner circle.
    • Parallelogram – If b is the base and h is the height of a parallelogram then
      •      Area = b*h
      •     Perimeter = 2*(b + h)
    • Rhombus – If a is the side & d1and d2are the diagonals of a rhombus then
      •       Area = ½ *d1*d2
      •       Perimeter = 4*a
  • Conversion table for revision of units conversion – Below table shows relationships between different units of the area which comes handy while solving problems:
1 centimeter   = 10 millimeter
1 decimeter    = 10 centimeter
1 meter   = 10 decimeter
1 decameter   = 10 meter
1 hectometer  = 10 decameter
1 kilometer  = 10 hectometer

Exercise Discussions of RS Aggarwal Solutions for Class 10 Chapter 15: Perimeter and Areas of Plane Figures

Exercise 15A 

The first exercise has 20 questions that need you to apply various formulas to find the area of a triangle given its sides or perimeter. Questions have different types of triangles like isosceles, equilateral, and right-angled triangles along with a combination of figures like a triangle inside a circle, etc. 

Exercise 15B

The second exercise with 37 questions revolves around finding the area or perimeter of a rectangle, trapezium, rhombus, parallelogram, quadrilateral, and square. There are some word problems like the cost of fencing a square plot or painting a rectangular floor is given and other values are to be found which involve finding area or perimeter.

Multiple-Choice Questions

The last exercise has 20 multiple-choice questions. You need to apply the formulas for area and perimeter for different figures like square, rectangle, equilateral triangle, and rhombus to solve these problems. Problems are not always straightforward and you might need to apply logic to get the required information.

Benefits of RS Aggarwal Solutions for Class 10 Chapter 15: Perimeter and Areas of Plane Figures by Instasolv

  • You can rest assured to master this topic if you are going through our RS Aggarwal Solutions for preparing for your board exams. 
  • Learning shortcut methods of doing a sum, tips and tricks to memorize important formulas, all this is needed to solve the problems related to this chapter quickly in a stressful exam environment. 
  • We completely ensure that by providing you with step by step solutions for all the exercises of the chapter with easy to understand explanations.