Each of our Ganita Prakash Class 6 Worksheet and Class 6 Maths Chapter 6 Perimeter and Area Worksheet with Answers Pdf focuses on conceptual clarity.
Class 6 Maths Chapter 6 Perimeter and Area Worksheet with Answers Pdf
Perimeter and Area Class 6 Maths Worksheet
Class 6 Maths Chapter 6 Worksheet with Answers – Class 6 Perimeter and Area Worksheet
A. Choose the correct option.
Question 1.
The distance travelled by Shaina if she takes three rounds of a square park of side 70 m.
(a) 860 m
(b) 840 m
(c) 480 m
(d) 800 m
Answer:
(b) 840 m
Question 2.
The perimeter of a rectangle is 42 cm and its length is 13 cm. Its breadth is
(a) 8 cm
(b) 7 cm
(c) 6 cm
(d) 5 cm
Answer:
(a) 8 cm
Question 3.
Area of a rectangular field is 78 sq. m. If the length of the field is 13 m, then its breadth is
(a) 6 m
(b) 8 m
(c) 11 m
(d) 12 m
Answer:
(a) 6 m
Question 4.
If the perimeter of a square is 36 m, then its area is
(a) 81 sq. m
(b) 56 sq. m
(c) 196 sq. m
(d) 49 sq. m
Answer:
(a) 81 sq. m
Question 5.
If m is the number of complete squares, n is the number of more than half squares, and p is the number of half squares that are enclosed by the irregular figure, then the area of the irregular figure by graph paper is
(a) m + n + \(\frac{1}{2}\)p sq. units
(b) m + \(\frac{1}{2}\)n + p sq. units
(c) \(\frac{1}{2}\)m + n + p sq. units
(d) m + \(\frac{1}{2}\)(n + p) sq.units
Answer:
(a) m + n + \(\frac{1}{2}\)p sq. units
Question 6.
If the area of a square is equal to its perimeter, then each side is
(a) 1 unit
(b) 2 units
(c) 3 units
(d) 4 units
Answer:
(d) 4 units
Question 7.
What will be the change in area of a rectangle if its length is doubled and its breadth is halved?
(a) becomes double
(b) becomes half
(c) remains the same
(d) none of these
Answer:
(c) remains the same
Assertion (A) & Reason (R) Questions.
Directions.: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is.the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
Question 1.
Assertion (A): Perimeter of a regular hexagon = 6 × length of its side.
Reason (R): Perimeter of a regular polygon = number of sides × length of its side.
Answer:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is.the correct explanation of Assertion (A).
Question 2.
Assertion (A): Area of a square is doubled if the side of the square is doubled.
Reason (R): Area of a square = side × side sq. units
Answer:
(d) Assertion (A) is false but Reason (R) is true.
Question 3.
Assertion (A): Area of a square is quadrupled if the side of the square is doubled.
Reason (R): Perimeter of a rectangle is the sum of the lengths of all its sides.
Answer:
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
B. Fill in the blanks.
1. The perimeter of a triangle with sides 5 cm, 6 cm, and 8 cm is _________.
Answer:
19 cm
2. The area of a square of side 7 cm is _________.
Answer:
49 sq.cm
3. The amount of region enclosed by a plane closed figure is called its _________.
Answer:
area
4. The area of a rectangle with length 5 cm and breadth 3 cm is _________.
Answer:
15 sq. cm
5. The perimeter of a rectangle is 30 cm and its length is 9 cm, then the breadth is _________.
Answer:
6 cm
C. Solve the following questions.
Question 1.
Manoj has a square shaped plot. He measured the distance around the plot as 150 wooden sticks. Later he found that the length of the stick was 54 cm. Find the side of the plot in metres. He wants to fence the plot with 3 rounds of wire. If the cost of fencing the wire is ₹ 18 per metre. What will be the total cost of fencing the plot?
Answer:
20.25 m, ₹ 4374
Question 2.
The length and the breadth of a rectangular sheet of paper are 20 cm and 10 cm, respectively. A rectangular piece is cut from the sheet as shown in the figure. Which of the following statements is correct for the remaining sheet?
(a) Perimeter remains the same, but area changes
(b) Area remains the same, but perimeter changes
(c) Both area and perimeter change
(d) Both area and perimeter remain the same
Answer:
(a) Perimeter remains the same, but area changes
Question 3.
Martsi warLts to make rectangular cards of dimenstons 18 cm x 12 cm. She has a square chart paper of side 72 cm. How many cards can she make from this chart? What area of the churt paper wilt be Left?
Answer:
24, No area of chart paper will be left.
Question 4.
Three squares are joined together as shown in the figure. Their sides are 4 cm, 10 cm, and 3 cm respectively. Find the perimeter of the figure.
Answer:
54 cm
Question 5.
Find the area of the given figure.
Answer:
290 sq.cm
HOTS Question
In the adjoining figure, all triangles are equilateral, and AB = 16 units. Other triangles have been formed by taking the midpoints of the sides. What is the perimeter of the figure?
Answer:
90 units
Fun time
Take a squared paper of 1 cm × 1 cm unit squares and trace your palm on it. Calculate th area enclosed by your palm..
Perimeter and Area
Hardik and Shreya are friends and study in the same class. Their math teacher has assigned a math project, making geometrical shapes using wires and finding their perimeters.
Shreya: Hardik! The dosed shapes that we are making using the piece of wire are polygons. Hardik: Yes, the folded parts of the wire are the sides of these polygons.
Shreya: How can we find the perimeters of these shapes?
Hardik: The perimeter of any closed figure is the total length of its boundary or the distance along the sides of the closed figure.
So, the perimeter of a polygon = sum of the lengths of its sides
Question 1.
Find the perimeter of the following polygons.
Answer:
(a) 19 cm
(b) 49 cm
Perimeter of a Triangle
A triangle Is a 3-sided polygon.
Perimeter off a triangle = Sum off the length off Its three sides.
For example,
PerlmeteroffatrlangleABC = (a + b + c) unlts
Perimeter of a Rectangle
A rectangle is a 4-sided closed plane figure whose opposite sides are of equal length and parallel to each other, and all 4 angles are right angles.
Perimeter of a rectangle = 2 × (length + breadth) units
For example,
Perimeter of the rectangle ABCD = 2 × (l + b) units
Perimeter of a Square
A square is a 4-sided regular polygon whose all four sides are of equal length and whose opposite sides are parallel to each other, and all four angles are 90°.
Perimeter of a square = 4 × length of its side
For example,
Perimeter of the square ABCD = 4 × a units
Question 2.
Find the perimeter of the following figures.
Answer:
(a) 22 cm
(b) 26 cm
(c) 16 cm
Question 3.
Find the perimeter of the rectangles of the following measures.
(a) Length = 12 cm, breadth = 8 cm
(b) Length = 144 cm, breadth = 92 cm
Answer:
(a) 40 cm
(b) 472 cm
Question 4.
Find the perimeter of the squares of the following measures of
(a) side = 12 cm
(b) side = 7m
Answer:
(a) 48 cm
(b) 28 m
Question 5.
Gayatri has participated in the Saj-Sajawat’ cornpetltion. held at her school. She decorates a rectangular tablecloth with a Lace border. If the table cloth is 2 cm Long and 80 cm wide, then find the required Length of the Lace.
Answer:
560 cm or 5m 60 cm
Question 6.
Arun’s father is very health conscious. He is used to going on the morning walk every day. During the morning waLk, he takes 4 rounds of a rectangular park whose length is 400 in and breadth is 100m. Find the distance covered by Arurt’s father during the morning walk on. a particular day.
Answer:
4000 m or 4 km
Question 7.
Kashi ruade two paintings, one in rectangular shape dimensions 80 cm × 50 cm, and the another in a square shape of side 80 cm. She wants to decorate the boundaries of the paintings by using co toured tape. Find the total length of the tape required. Which painting required more tape than the other?
Answer:
580 cm, squared painting
Question 8.
A wire of length 70 m is to be used to form squares of side length 35 cm. How many squares can be formed out of it?
Answer:
50
Question 9.
The perimeter of a square of side 13 cm is equal to the perimeter of a rectangle whose breadth is 8 cm. Find the length of the rectangle.
Answer:
18 cm
Question 10.
Find the perimeter of each of the following figures if each small box is a square of 1 unit.
Answer:
(a) 28 units
(b) 34 units
Question 11.
As shown in the figure, Tanisha and Tanya start running along the rectangular track from the marked points. Tanisha runs along the outer boundary of the track and completes 4 rounds while Tanya runs along the inner boundary of the track and completes 6 rounds. Find out who ran the longer distance and by how much.
Answer:
Tanya, 160 m
Perimeter of Regular Polygons
Polygons having all sides of equal lengths are called regular polygons. Equilateral triangles, squares, etc. are some examples of regular polygons. The perimeter of a regular polygon = number of sides x length of the side.
Perimeter of an Equilateral Triangle
A triangle having three equal sides is called an equilateral triangle. Therefore, the perimeter of an equilateral triangle = 3 x length of its side. If the length of the side of an equilateral triangle is a unit, then the perimeter of the equilateral triangle = _________ units
Question 12.
Find the perimeter of the following equilateral triangles.
Answer:
(a) 9 cm
(b) 15 cm
Question 13.
A piece of wire is 72 cm long. Wkat will be tke length of each side if it is used to form:
(a) A square
(b) A regular pentagon
Answer:
(a) 18 cm
(b) 14\(\frac{2}{5}\) cm
Question 14.
Find out which of the following has the largest perimeter:
(a) An equilateral triangle of side 10 cm
(b) A square of side 15 cm
(c) A regular pentagon of side 9 cm
(d) A regular hexagon of side 8 cm
Answer:
(b) A square of side 15 cm
Think and Answer
Four regular hexagons are drawn so as to form the design as shown in the figure. If the perimeter of the design is 28 cm, find the length of each side of the regular hexagon.
Answer:
2 cm
SPLIT AND JOIN
Question 15.
Raski takes a rectangular piece of paper of dimension 9 cm x 6 cm and ske cuts it into two equal pieces. Then she joins these two pieces in different wags and tries to find their perimeters. Help her to compute the perimeters of each of the following arrangements.
Answer:
(a) 36 cm
(b) 36 cm
(c) 42 cm
(d) 46 cm
(e) Can you arrange the two pieces to form a figure with a perimeter of 40 cm? if yes, then arrange.
Answer:
Yes
Area
The amount of surface enclosed by a closed figure is called its area. It is measured in square units. Area of a rectangle: The product of the length and the breadth of a rectangle is called the area of the rectangle.
Thus, the area of a rectangle = length × breadth sq. units
Or area of a rectangle = l × b sq. units
(Where l and b are the length and the breadth of the rectangle respectively)
Area of a square: A square has all four sides of equal length.
Therefore, l = b = a (let), where a is the length of each side of the square.
Therefore, the area of the square = side × side sq. units
Or area of the square = a × a sq. units
Question 16.
Find the area of the following rectangles:
(a) Length = 75 cm, breadth = 35 cm
(b) Length = 1 m, breadth = 70 cm
Answer:
(a) 2625 sq. cm
(b) 7000 sq. cm
Question 17.
Find the area of the following squares, the length of whose sides are:
(a) 18 cm
(b) 19 mm
Answer:
(a) 324 sq. cm
(b) 361 sq. mm
Question 18.
The length and the breadth of a rectangular garden are 115 m and 72 m. What is its area? What will be the cost of laying the grass in the garden at the rate of ₹ 0.25 per sq. m?
Answer:
8280 sq. m; ₹ 2070
Question 19.
Find the area of a square whose perimeter is 108 cm.
Answer:
729 sq. cm
Question 20.
The area of a rectangular piece of cardboard is 144 sq. cm and its Length is 24 cm. What is the width of the cardboard?
Answer:
6 cm
Question 21.
Priya decided to embroider her square-shaped handkerchief of dimensions 20 cm × 20 cm using a new embroidery technique she learnt from her mother. If 1 reel of thread can cover an area of 10 sq. cm, then how many reels of thread will Priya need to embroider her handkerchief completely?
Answer:
40 reels
Question 22.
Aakriti has pasted 8 stamps along the length and 5 stamps along the breadth of a rectangular paper sheet. She wants to know the number of stamps required to fill the area of the given sheet completely. The dimensions of the stamp are 2 cm × 2 cm. How many stamps are required to cover the sheet completely?
Answer:
40 stamps
Area of Irregular Shapes
The area of Irregular closed shapes can be found out by using the formula given below.
Area enclosed under the figure = Number of complete squares (m) + Number of more than half squares (n) + \(\frac{1}{2}\) × Number of half squares (p)
Question 23.
Find the area of the following closed figures.
(a) ____________________________________
(b) ____________________________________
Answer:
(a) 33 sq. units
(b) 13 sq. units
Area of a Triangle
Since the diagonal of a rectangle divides it into two equal halves, and each half is a triangle.
So, the area of a triangle = \(\frac{1}{2}\) × area of a rectangle
Question 24.
Find the area of triangle in each figure.
(a) ____________________________________
(b) ____________________________________
Answer:
(a) 25 sq. units
(b) 33 sq. units
Question 25.
Find the areas of the figures given below by dividing them into rectangles and triangles.
(a) ____________________________________
(b) ____________________________________
(c) ____________________________________
Answer:
(a) 10.5 sq. units
(b) 17 sq. units
(c) 14 sq. units