RBSE Solutions Class 6 Maths Chapter 14 Perimeter and Area Important Questions

Rajasthan Board RBSE Class 6 Maths Chapter 14 Perimeter and Area Additional Questions

Multiple Choice Questions

 

Question 1. Length of a rectangular park is L and breadth is B, then its area will be
(a) \( 2 \times (L + B) \)
(b) \( 2 \times (L - B) \)
(c) \( 2 \times (L \div B) \)
(d) \( L \times B \)
Answer: (d) \( L \times B \)
In simple words: To find the area of a rectangle, you just multiply its length by its breadth. This gives you the total space inside the shape.

🎯 Exam Tip: Remember that "area" involves multiplication of two dimensions, while "perimeter" involves adding up all the sides.

 

Question 2. Distance covered in a complete round of a squared field will be
(a) \( 4 \times \text{side} \)
(b) \( (\text{side})^2 \)
(c) \( \text{side} \div 4 \)
(d) \( 4 \times \text{side}^2 \)
Answer: (a) \( 4 \times \text{side} \)
In simple words: When you walk one full round around a square field, you cover the distance of all its four sides added together. Since all sides are equal, it's four times the length of one side.

🎯 Exam Tip: The distance around a shape is its perimeter. For a square, perimeter is \( 4 \times \text{side} \), while area is \( \text{side} \times \text{side} \).

 

Question 3. Length of a rectangular lawn is 25 m and breadth is 15 m, then its area will be
(a) 80 sq. cm
(b) 375 sq. cm
(c) 40 sq. cm
(d) 100 sq. cm
Answer: (b) 375 sq. cm
In simple words: To find the area of the lawn, you multiply its length (25m) by its breadth (15m). This calculation gives 375 square meters. However, the options are in square centimeters, indicating a potential unit mismatch or just a standard way to present options.

🎯 Exam Tip: Always double-check the units given in the question and options. If they don't match, carefully convert them to avoid mistakes.

 

Question 4. Side of a square figure is 15 cm, then its area will be
(a) 225 sq. cm
(b) 60 sq. cm
Answer: (a) 225 sq. cm
In simple words: The area of a square is found by multiplying the side length by itself. So, for a 15 cm side, the area is \( 15 \times 15 = 225 \) square centimeters.

🎯 Exam Tip: Make sure to distinguish between perimeter (adding sides) and area (multiplying sides) when solving problems involving squares and rectangles.

 

Question 5. Side of a square field is 9 m, and it is to be fenced once with wire, then total length of required wire will be
(a) 80 m
(b) 160 m
(c) 36 m
(d) 18 m
Answer: (c) 36 m
In simple words: To fence a square field once, you need a wire length equal to its perimeter. If one side is 9 meters, the perimeter is 4 times 9 meters, which is 36 meters.

🎯 Exam Tip: When a question involves fencing, it typically asks for the perimeter of the shape. If it mentions multiple rows of fencing, multiply the perimeter by the number of rows.

 

Question 6. Sides of a triangle are 10 cm, 8 cm and 5 cm, then perimeter of triangle will be
(a) 40.5 cm
(b) 23 cm
(c) 22 cm
(d) 20 cm
Answer: (b) 23 cm
In simple words: The perimeter of any shape is found by adding up the lengths of all its sides. For this triangle, you add 10 cm, 8 cm, and 5 cm together to get the total perimeter.

🎯 Exam Tip: For any polygon, the perimeter is simply the sum of the lengths of all its sides. Do not multiply or use formulas for areas unless asked.

 

Question 7. Perimeter of square
(a) \( 4 \times (\text{length of side}) \)
(b) \( 2 + (l + b) \)
(c) \( 2 \times (l + b) \)
(d) Product of four sides
Answer: (a) \( 4 \times (\text{length of side}) \)
In simple words: A square has four sides that are all the same length. So, to find its perimeter, you just multiply the length of one side by four.

🎯 Exam Tip: Options (b) and (c) represent the perimeter of a rectangle, which has different formulas because its length and breadth are usually not equal.

 

Question 1. Fill in the blanks:
(i) Area of square is \( \text{side} \times \text{side} \).
(ii) Perimeter of equilateral triangle is \( 3 \times \) length of side.
(iii) A figure which has all sides and angles equal, is called a regular polygon.
Answer:
(i) The area of a square is calculated by multiplying its side length by itself, which can be written as \( \text{side} \times \text{side} \) or \( \text{side}^2 \). It measures the space inside the square.
(ii) An equilateral triangle has three sides of equal length. Its perimeter is found by adding these three equal sides, so it is \( 3 \times \) the length of one side. This makes sense as 'equi' means equal and 'lateral' means side.
(iii) A figure that has all its sides and all its angles equal is known as a regular polygon. Examples include a square (a regular quadrilateral) or a regular hexagon. Regular shapes are symmetrical.
In simple words: The space inside a square is its side multiplied by itself. An equilateral triangle's boundary is three times one side. A shape with all equal sides and angles is called a regular polygon.

🎯 Exam Tip: Understand the basic definitions for geometric shapes. "Equilateral" means equal sides, "regular" means equal sides and equal angles.

 

Very Short Answer Type Questions

 

Question 1. What is Area?
Answer: Area is the amount of flat space covered or enclosed within a two-dimensional closed figure. It tells us how much surface the figure takes up. We measure area in square units, like square centimeters or square meters.
In simple words: Area is how much space is inside a shape.

🎯 Exam Tip: Define area clearly as "the amount of surface enclosed" or "the space occupied by a two-dimensional shape."

 

Question 2. What are regular figures?
Answer: Regular figures, also known as regular polygons, are shapes where all their sides are the same length, and all their angles are equal in measure. For example, a square is a regular figure. These shapes have a balanced and symmetrical look.
In simple words: Regular figures are shapes that have all sides and all angles equal.

🎯 Exam Tip: When defining regular figures, mention both "all sides equal" and "all angles equal" for a complete answer.

 

Question 3. What is Perimeter?
Answer: Perimeter is the total distance around the outside edge or boundary of a closed two-dimensional figure. Imagine walking around the shape once; the total distance you walk is its perimeter. It is measured in linear units like meters or centimeters.
In simple words: Perimeter is the total distance around the edge of a shape.

🎯 Exam Tip: Clearly state that perimeter is the "distance covered along the boundary" or "the total length of the boundary."

 

Question 4. Find the perimeter of a regular pentagon, whose each side is of length 3 cm.
Answer: A regular pentagon is a shape with five sides, and all these sides are equal in length. Since each side is 3 cm long, we find its perimeter by adding the length of all five sides. So, the perimeter is \( 5 \times 3 \text{ cm} = 15 \text{ cm} \). This is a simple multiplication.
In simple words: A pentagon has 5 equal sides. So, multiply 5 by the side length (3 cm) to get the perimeter (15 cm).

🎯 Exam Tip: Remember that "penta" means five, so a pentagon always has five sides. For a regular polygon, multiply the number of sides by the length of one side to find the perimeter.

 

Short/Long Answer Type Questions

 

Question 1. Find the area of triangle given in figure.
Answer: The problem describes finding the area of a triangle by counting squares on a grid, which is a common method when a figure is drawn on squared paper. We count the number of full squares completely inside the triangle, which is 27. Then, we count squares that are half or more than half covered by the triangle, which is 9. Adding these gives the approximate area. Therefore, the area of the triangle is \( 27 + 9 = 36 \) square units. This method helps estimate areas of irregular shapes.
In simple words: Count all the full squares inside the triangle. Then count squares that are half or more covered. Add these two numbers together to get the total area in square units.

🎯 Exam Tip: When using the grid method for area, remember to count squares that are exactly half or more than half as one full square, and ignore squares less than half covered.

 

Question 2. Length and breadth of a farmer's field are 240 m and 180 m respectively. He wants to fence his field thrice by a rope. What is the total length of rope he must use?
Answer: First, we need to find the perimeter of the rectangular field, which is the distance around it. The formula for the perimeter of a rectangle is \( 2 \times (\text{length} + \text{breadth}) \).
Perimeter of field \( = 2 \times (240 \text{ m} + 180 \text{ m}) \)
\( = 2 \times 420 \text{ m} \)
\( = 840 \text{ m} \)
Since the farmer wants to fence the field three times, the total length of rope needed will be three times the perimeter. So, \( \text{Total length of rope} = 3 \times 840 \text{ m} = 2520 \text{ m} \). Fencing is a practical application of perimeter.
In simple words: First, find the distance around the field (perimeter) by adding length and breadth, then multiplying by 2. Then, multiply this perimeter by 3 because the farmer wants to fence it three times.

🎯 Exam Tip: When calculating total fencing, always find the perimeter first, and then multiply by the number of times the field is to be fenced.

 

Question 3. Find the area of an iron rod in sq. m, whose length is 2 m 30 cm and breadth is 1 m 20 cm.
Answer: To find the area, we first need to convert all measurements to the same unit, meters. Since 100 cm equals 1 meter, 30 cm is 0.30 m and 20 cm is 0.20 m.
Length of iron rod \( = 2 \text{ m} + 30 \text{ cm} = 2 \text{ m} + 0.30 \text{ m} = 2.30 \text{ m} \)
Breadth of iron rod \( = 1 \text{ m} + 20 \text{ cm} = 1 \text{ m} + 0.20 \text{ m} = 1.20 \text{ m} \)
Now, we calculate the area using the formula for a rectangle, Area \( = \text{length} \times \text{breadth} \).
Area of iron rod \( = 2.30 \text{ m} \times 1.20 \text{ m} = 2.76 \text{ sq. m} \). It's crucial to use consistent units for calculation.
In simple words: Change centimeters to meters first. So, 2m 30cm becomes 2.30m, and 1m 20cm becomes 1.20m. Then, multiply the length by the breadth to get the area in square meters.

🎯 Exam Tip: Always convert all units to a consistent standard (e.g., all to meters or all to centimeters) before performing calculations to avoid errors.

 

Question 4. Length and breadth of a rectangular field are 0.7 km and 0.5 km respectively. We have to fence this field with a wire in 4 rows. What is the total length of wire we must use?
Answer: First, we find the perimeter of the rectangular field. The formula is \( 2 \times (\text{length} + \text{breadth}) \).
Perimeter of field \( = 2 \times (0.7 \text{ km} + 0.5 \text{ km}) \)
\( = 2 \times 1.2 \text{ km} \)
\( = 2.4 \text{ km} \)
Since the field needs to be fenced with wire in 4 rows, we multiply the perimeter by 4 to get the total length of wire required. So, \( \text{Total length of wire} = 4 \times 2.4 \text{ km} = 9.6 \text{ km} \). This calculation ensures enough wire is bought for all rows.
In simple words: First, add the length and breadth, then multiply by 2 to get the perimeter of the field. After that, multiply the perimeter by 4 because the wire will be used for 4 rows.

🎯 Exam Tip: When fencing with multiple rows, calculate the perimeter for one row first, and then multiply that by the number of rows to get the total length of material needed.

 

Question 5. Length of a piece of string is 30 cm. What will be the length of each side, if we made by string
(a) a square
(b) an equilateral triangle
Answer: The total length of the string will become the perimeter of the shape formed.
(a) If a square is made from the string, its perimeter will be 30 cm. A square has 4 equal sides. To find the length of one side, we divide the total perimeter by 4.
\( \text{Length of one side of square} = \frac{\text{Perimeter}}{4} = \frac{30 \text{ cm}}{4} = 7.5 \text{ cm} \). Each side will be 7.5 cm long.
(b) If an equilateral triangle is made, its perimeter will also be 30 cm. An equilateral triangle has 3 equal sides. To find the length of one side, we divide the total perimeter by 3.
\( \text{Length of one side of equilateral triangle} = \frac{\text{Perimeter}}{3} = \frac{30 \text{ cm}}{3} = 10 \text{ cm} \). Each side will be 10 cm long, showing how the same length of string can make different side lengths for different shapes.
In simple words: The string's length is the perimeter. For a square, divide 30 cm by 4 to get each side. For an equilateral triangle, divide 30 cm by 3 to get each side.

🎯 Exam Tip: Remember the number of equal sides for common regular polygons: square (4 sides), equilateral triangle (3 sides), regular pentagon (5 sides), regular hexagon (6 sides).

 

Question 6. Find the area of the given composite figure by breaking it into rectangles A, B, and C. Measurements of sides are given in cm.

Answer: We find the area of the given composite figure by dividing it into three simple rectangles labeled A, B, and C. The total area will be the sum of the areas of these individual rectangles. Area of rectangle (A) \( = (2 \times 1) = 2 \text{ sq. cm} \) Area of rectangle (B) \( = (5 \times 1) = 5 \text{ sq. cm} \) The solution provided only specifies the areas for rectangles A and B. Assuming these are the primary components mentioned, the total area would be calculated by summing the areas of all such decomposed parts. The idea is to break complex shapes into simpler ones to easily calculate their area.In simple words: Break the big shape into smaller, easy-to-measure rectangles (like A and B). Find the area of each small rectangle, and then add them up to get the total area of the whole figure.

🎯 Exam Tip: For complex or irregular shapes, the best strategy is often to decompose them into simpler, familiar shapes (like rectangles or triangles), calculate the area of each, and then add them to find the total area.