CBSE Class 6 Mathematics Perimeter and Area Worksheet Set 01

Very Short Answer Questions

Question 1. Define the perimeter of a closed plane figure.
Answer:
The perimeter of a closed plane figure is the distance covered along its boundary when we go around it once.

Teacher's Note:
1. Use the words 'boundary' and 'once'.
2. It is a length.

Question 2. Write the rule for finding the perimeter of a polygon.
Answer:
Perimeter of a polygon = sum of the lengths of all its sides.

Teacher's Note:
1. A polygon is made only of line segments.
2. Do not miss any side.

Question 3. Write the formula for the perimeter of a rectangle whose length and breadth are known.
Answer:
Perimeter of a rectangle = 2 × (length + breadth).

Teacher's Note:
1. Two lengths and two breadths.
2. Add first, then double.

Question 4. Find the perimeter of a square photo frame whose side is 12 cm.
Answer:
Perimeter = 4 × side = 4 × 12 = 48 cm.

Teacher's Note:
1. A square has four equal sides.
2. Perimeter is in cm, not sq cm.

Question 5. What is meant by the area of a closed figure?
Answer:
The area of a closed figure is the amount of region enclosed by it, found by counting how many unit squares cover it.

Teacher's Note:
1. Area is about the inside.
2. Perimeter is about the boundary.

Question 6. In which kind of units is area measured? Give one example of such a unit.
Answer:
Area is measured in square units, for example square centimetres (sq cm) or square metres (sq m).

Teacher's Note:
1. Never write an area in cm or m.
2. One example is enough.

Question 7. A rectangular carpet is 9 m long and 6 m wide. Find its area.
Answer:
Area = length × breadth = 9 × 6 = 54 sq m.

Teacher's Note:
1. Multiply for area.
2. Write the unit as sq m.

Question 8. Find the area of a square tile whose side is 7 cm.
Answer:
Area = side × side = 7 × 7 = 49 sq cm.

Teacher's Note:
1. Side times side, not 4 times side.
2. Unit: sq cm.

Question 9. An equilateral triangle has a side of length 11 cm. Find its perimeter.
Answer:
All three sides are equal, so perimeter = 3 × 11 = 33 cm.

Teacher's Note:
1. Equilateral means all sides equal.
2. 3 × side.

Question 10. What is a regular polygon? Write the rule for the perimeter of a regular polygon.
Answer:
A regular polygon is a closed figure with all sides equal and all angles equal.
Its perimeter = (number of sides) × (length of one side).

Teacher's Note:
1. Square and equilateral triangle are regular polygons.
2. Both sides and angles must be equal.

Question 11. Meena draws a coloured border all around a square rangoli. Is she finding the perimeter or the area of the rangoli?
Answer:
She is finding the perimeter, because the border runs along the boundary of the rangoli.

Teacher's Note:
1. Border means boundary.
2. Filling the inside would need area.

Question 12. A triangle is drawn inside a rectangle with its base along one side of the rectangle. How is the area of this triangle related to the area of the rectangle?
Answer:
The area of the triangle is half the area of the rectangle that encloses it.

Teacher's Note:
1. Its third corner is on the opposite side.
2. This leads to ½ × base × height.

Question 13. The perimeter of a rectangular notebook cover is 36 cm and its length is 11 cm. Find its breadth.
Answer:
Length + breadth = 36 ÷ 2 = 18 cm.
Breadth = 18 − 11 = 7 cm.

Teacher's Note:
1. Halve the perimeter first.
2. Then subtract the length.

Question 14. The perimeter of a square park is 52 m. Find the length of one side of the park.
Answer:
Side = perimeter ÷ 4 = 52 ÷ 4 = 13 m.

Teacher's Note:
1. Undo 4 × side by dividing by 4.
2. Check: 4 × 13 = 52.

Question 15. Two sides of a triangular park measure 13 m and 17 m. If the perimeter of the park is 44 m, find the third side.
Answer:
Third side = 44 − (13 + 17) = 44 − 30 = 14 m.

Teacher's Note:
1. Add the known sides, then subtract from the perimeter.
2. Check: 13 + 17 + 14 = 44.

Question 16. A rectangular kitchen garden is 20 m long and has an area of 240 sq m. Find its width.
Answer:
Width = area ÷ length = 240 ÷ 20 = 12 m.

Teacher's Note:
1. Divide area by the known side.
2. The answer is a length, so the unit is m.

Question 17. A farmer ties a rope twice all around a rectangular field that is 90 m long and 60 m wide. What total length of rope does he need?
Answer:
One round = 2 × (90 + 60) = 300 m.
Two rounds = 2 × 300 = 600 m.

Teacher's Note:
1. Find one round first.
2. Then multiply by the number of rounds.

Question 18. A string of length 48 cm is bent to form a regular hexagon. Find the length of each side.
Answer:
A regular hexagon has 6 equal sides, so each side = 48 ÷ 6 = 8 cm.

Teacher's Note:
1. The string's length is the perimeter.
2. Divide by the number of sides.

Question 19. A shape traced on graph paper covers 8 full squares and 6 exactly half squares. Find its area in square units.
Answer:
Area = 8 + 6 × \( \frac{1}{2} \) = 8 + 3 = 11 square units.

Teacher's Note:
1. Each exactly-half square counts as ½.
2. Two halves make one.

Question 20. A right triangle has a base of 10 cm and a height of 6 cm. Find its area.
Answer:
Area = \( \frac{1}{2} \) × base × height = \( \frac{1}{2} \) × 10 × 6 = 30 sq cm.

Teacher's Note:
1. The triangle is half of a 10 × 6 rectangle.
2. 60 ÷ 2 = 30.

Question 21. The floor of a store room is 7 m by 5 m. A square mat of side 3 m is spread on it. Find the area of the floor that is still uncovered.
Answer:
Floor = 7 × 5 = 35 sq m; mat = 3 × 3 = 9 sq m.
Uncovered area = 35 − 9 = 26 sq m.

Teacher's Note:
1. Whole minus covered.
2. Use area, not perimeter.

Question 22. Find the cost of tiling a rectangular plot 40 m long and 25 m wide at the rate of Rs 9 per square metre.
Answer:
Area = 40 × 25 = 1000 sq m.
Cost = 1000 × 9 = Rs 9,000.

Teacher's Note:
1. Tiling covers the inside, so use area.
2. Rate is per square metre.

Question 23. The boundary of a shape drawn on a square grid is made of 6 straight unit lines and 3 diagonal unit lines. Is its perimeter equal to 9 units? Give a reason.
Answer:
No. A diagonal unit line is longer than a straight unit line, so the perimeter is more than 9 units. It is written as 6s + 3d units.

Teacher's Note:
1. s = straight unit, d = diagonal unit.
2. A slanting line across a square is longer than its side.

Question 24. Name the shape that is used as the standard unit for measuring area, and give one reason for choosing it.
Answer:
The square is used. Squares fit together without gaps or overlaps, so they can be counted exactly.

Teacher's Note:
1. Circles leave gaps between them.
2. That is why we say 'square units'.

Question 25. Give the sides of two different rectangles that both have an area of 36 square units but have different perimeters. Write both perimeters.
Answer:
A 6 × 6 square: area 36 square units, perimeter 24 units.
A 12 × 3 rectangle: area 36 square units, perimeter 30 units.

Teacher's Note:
1. Find two factor pairs of 36.
2. Other answers like 9 × 4 or 18 × 2 are also correct.

Question 26. A rectangular floor 9 m long and 7 m wide is divided by one straight line into two smaller rectangles. One of them measures 9 m by 3 m. Find the area of the other rectangle.
Answer:
Whole floor = 9 × 7 = 63 sq m; given part = 9 × 3 = 27 sq m.
Other rectangle = 63 − 27 = 36 sq m (it is 9 m by 4 m).

Teacher's Note:
1. Parts add up to the whole.
2. Check: 9 × 4 = 36.

Question 27. A figure made of unit squares has a perimeter of 24 units. How should one more unit square be attached so that the perimeter remains 24 units?
Answer:
Fit the new square into a notch so that it touches the figure along two full sides.
Then 4 edges are added and 4 edges get hidden, so the perimeter stays 24 units.

Teacher's Note:
1. One side touching adds 2 units.
2. Three sides touching removes 2 units.

Question 28. A triangular sail has a base of 12 cm and a height of 7 cm in a drawing. Using the idea of the enclosing rectangle, find the area of the sail.
Answer:
Enclosing rectangle = 12 × 7 = 84 sq cm.
Sail = half of it = 84 ÷ 2 = 42 sq cm.

Teacher's Note:
1. A triangle is half its enclosing rectangle.
2. Same as ½ × base × height.

Question 29. Shape A has an area of 18 square units and Shape B has an area of 20 square units, yet Shape A has the longer perimeter. Give one pair of rectangles that fits this description.
Answer:
Shape A: a 1 × 18 rectangle, area 18 square units, perimeter 38 units.
Shape B: a 5 × 4 rectangle, area 20 square units, perimeter 18 units.

Teacher's Note:
1. Make A long and thin.
2. Make B nearly square.

Question 30. A square sheet of side 10 cm is folded in half and cut along the fold into two equal rectangles. Compare the total perimeter of the two rectangles with the perimeter of the original square.
Answer:
Square: 4 × 10 = 40 cm. Each rectangle is 10 cm × 5 cm with perimeter 30 cm.
Together: 60 cm, which is 1\( \frac{1}{2} \) times the perimeter of the square (20 cm more).

Teacher's Note:
1. The cut makes two new 10 cm edges.
2. Area stays the same; perimeter grows.