NCERT MCQ Solutions for Class 6 Maths Chapter 6 Perimeter and Area

The perimeter measures the complete boundary of a closed figure. For a polygon, I add the lengths of all its sides. The region inside the boundary is measured by area, so perimeter and area describe different things.

Perimeter = 2 × (Length + Breadth)
= 2 × (12 + 8)
= 2 × 20 = 40 cm
The rectangle has two sides of each length, so both pairs of opposite sides are included.

A square has four equal sides.
Tape needed = Perimeter = 4 × Side
= 4 × 1 = 4 m
The tape follows all four sides of the frame, so one side length alone is not enough.

Perimeter of the triangle = Sum of its three side lengths
= 4 + 5 + 7
= 16 cm
The sides have different lengths, so I add the three given measurements rather than multiplying one of them by 3.

Lace required = Perimeter of the tablecloth
= 2 × (3 + 2)
= 10 m
The lace runs around the boundary. Multiplying 3 by 2 would give its area in square metres, not the length of lace.

The perimeter of a rectangle = sum of all four sides
Or 2 × (length + breadth)
Or 2 × (l + b)

Perimeter a square = 4 × side
Here, side of square = 4 m
∴ Perimeter = 4 × 4 = 16 cm

Length + Breadth = Perimeter ÷ 2
= 14 ÷ 2 = 7 cm
Length = 7 − 2 = 5 cm
Check: 2 × (5 + 2) = 14 cm, which matches the given perimeter.

Length of wire = 2 × (5 + 3) = 16 cm
The square has the same perimeter because the wire length does not change.
Side of square = 16 ÷ 4 = 4 cm.

Sum of the two known sides = 20 + 14 = 34 cm
Third side = 55 − 34 = 21 cm
Check: 20 + 14 + 21 = 55 cm. Thus, all three sides together give the required perimeter.

Perimeter = 2 × (150 + 120) = 540 m
Cost = 540 × ₹40
= ₹21,600
Fencing depends on the boundary length. The area of the park is not needed because the charge is per metre of fence.

One round = 2 × (230 + 160)
= 2 × 390 = 780 m
Three rounds = 3 × 780 = 2340 m
Each round follows the same boundary, so the perimeter is multiplied by 3.

Area of a rectangle = Length × breadth
Or = l × b

Perimeter of a triangle = sum of all three sides
Here, sides of triangle = 5 cm, 6 cm, and 7 cm.
∴ Perimeter of a triangle = 5 + 6 + 7 = 18 cm

Akshi’s distance = 5 × 2 × (70 + 40) = 1100 m
Toshi’s distance = 7 × 2 × (60 + 30) = 1260 m
Difference = 1260 − 1100 = 160 m
Toshi runs farther even though her track is smaller.

A regular hexagon has 6 equal sides.
Side length = Perimeter ÷ 6
= 36 ÷ 6 = 6 cm
Check: 6 × 6 = 36 cm, so all six sides use the whole string.

A square’s diagonal is longer than its side, so d > s.
Therefore, 3d > 3s.
6s + 3d > 6s + 3s = 9s
Counting each diagonal as one side-length would underestimate the perimeter.

The joined rectangle has length 6 + 6 = 12 cm and width 2 cm.
Perimeter = 2 × (12 + 2) = 28 cm
The joined edges lie inside the new shape, so they are not part of its outer boundary.

Original area = 6 × 4 = 24 cm²
Rearranging uses the same two pieces without losing or overlapping any part. Therefore, the total area remains 24 cm², although the new boundary and its perimeter may be different.

Area of a square = side²
Here side of square = 5 m
∴ Area of a square = 5² = 25 sq. m

Perimeter of a square = sum of all four sides
Or = 4 × side (Because all sides of a square are equal)

Floor area = 5 × 4 = 20 m²
Carpet area = 3 × 3 = 9 m²
Uncovered area = 20 − 9 = 11 m²
The carpet’s area is subtracted from the whole floor area.

Plot area = 12 × 10 = 120 m²
Area of four beds = 4 × (4 × 4) = 64 m²
Remaining area = 120 − 64 = 56 m²
All four beds are included before finding the area left over.

Area = Length × Width
Width = Area ÷ Length
= 300 ÷ 25 = 12 m
Check: 25 × 12 = 300 m². The width is a length, so its unit is metres rather than square metres.

Area = 500 × 200 = 1,00,000 m²
Number of 100 m² units = 1,00,000 ÷ 100 = 1000
Cost = 1000 × ₹8 = ₹8000
The rate applies to each 100 m², not to each single square metre.

Total area = 100 × 50 = 5000 m²
Number of allotments = 5000 ÷ 25
= 200
Thus, the available area can provide 200 allotments of 25 m² each, with no area left over.

An equilateral triangle has all three sides equal
∴ perimeter of equilateral triangle = 3 × length of one side

Square is formed by 36 cm long string this means perimeter of square is 36 cm.
∴ one side of square = 36/4 = 9 cm

The perimeters are:
4 by 6: 2 × (4 + 6) = 20 units
1 by 24: 50 units; 2 by 12: 28 units; 3 by 8: 22 units
The smallest is 20 units, for the 4 by 6 rectangle.

Rectangle area = 6 × 4 = 24 square units
A diagonal divides the rectangle into two triangles of equal area.
Area of each triangle = 24 ÷ 2 = 12 square units
Together, their areas add back to the original rectangle’s area.

Area of complete squares = 8 square units
Area of the two half-squares = 1/2 + 1/2 = 1 square unit
Total area = 8 + 1 = 9 square units
The half-squares combine to make one complete square.

The new square adds three exposed sides to the boundary. The side of the original figure that it touches is no longer exposed.
Change in perimeter = 3 − 1 = 2 units
Therefore, the perimeter increases by 2 units.

The row forms a rectangle 9 units long and 1 unit wide.
Perimeter = 2 × (9 + 1)
= 20 units
The shared edges between neighbouring squares are inside the rectangle and do not contribute to its perimeter.

Areas: 35 × 30 = 1050 ft² and 42 × 25 = 1050 ft²
Perimeters: 2 × 65 = 130 ft and 2 × 67 = 134 ft
Difference in perimeters = 134 − 130 = 4 ft
Equal area does not necessarily mean equal perimeter.

Other side = Area ÷ Known side
= 180 ÷ 15
= 12 ft
Check: 15 × 12 = 180 ft². Dividing the area by one side gives the length of the side perpendicular to it.

Garden area = 15 × 12 = 180 m²
Area of four beds = 4 × (2 × 1) = 8 m²
Lawn area = 180 − 8 = 172 m²
The four beds together, rather than just one bed, are removed from the garden area.

Outer area = 12 × 8 = 96 square units
Inner area = Half of outer area
= 96 ÷ 2 = 48 square units
Its length and width may vary, but their product must be 48 square units.

Let the square’s side be s. Its perimeter is 4s.
Each rectangle has sides s and s/2, so its perimeter is 2 × (s + s/2) = 3s.
Combined perimeter = 6s = 1½ × 4s.
The cut creates two new boundary edges.

Area of a rectangle = l × b
Here 𝑙 = 10𝑚 and b=5m
∴ Area = 10 × 5 = 50 sq. m

A hexagon has 6 sides
Perimeter of hexagon = 6 × side (In case of regular hexagon)
∴ one side = perimeter / 6 = 24 /6 = 4 cm