CBSE Class 6 Mathematics Chapter 10: Mensuration NCERT Solutions

The perimeter of a figure is the total length of its boundary. To find the perimeter, we sum the lengths of all its sides.

(a) For the triangle with sides 4 cm, 2 cm, and 1 cm:

Perimeter = Sum of all sides = 4 cm + 2 cm + 1 cm + 5 cm = 12 cm.

(b) For the regular pentagon with each side measuring 3 cm:

A regular pentagon has 5 equal sides. So, Perimeter = 5 × side length = 5 × 3 cm = 15 cm.

(c) For the square with each side measuring 15 cm:

A square has 4 equal sides. So, Perimeter = 4 × side length = 4 × 15 cm = 60 cm.

(d) For the rectangle with length 40 cm and breadth 4 cm:

Perimeter of a rectangle = 2 × (length + breadth) = 2 × (40 cm + 4 cm) = 2 × 44 cm = 88 cm.

(e) For the irregular polygon with sides 1 cm, 4 cm, 0.5 cm, 2.5 cm, 2.5 cm, 0.5 cm, and 4 cm:

Perimeter = Sum of all sides = 1 cm + 4 cm + 0.5 cm + 2.5 cm + 2.5 cm + 0.5 cm + 4 cm = 15 cm.

(f) For the polygon with the given sides:

Perimeter = Sum of all sides = 4 cm + 1 cm + 3 cm + 2 cm + 3 cm + 4 cm + 1 cm + 3 cm + 2 cm + 3 cm + 4 cm + 1 cm + 3 cm + 2 cm + 3 cm + 4 cm + 1 cm + 3 cm + 2 cm + 3 cm = 52 cm.

The length of the tape required to seal the rectangular box lid all around is equal to the perimeter of the rectangle.

Given: Length = 40 cm, Breadth = 10 cm.

The formula for the perimeter of a rectangle is:

$$P\; =\; 2\; \backslash times\; (\backslash text\{length\}\; +\; \backslash text\{breadth\})$$

Substituting the given values:

$$P\; =\; 2\; \backslash times\; (40\; \backslash text\{\; cm\}\; +\; 10\; \backslash text\{\; cm\})$$

$$P\; =\; 2\; \backslash times\; (50\; \backslash text\{\; cm\})$$

$$P\; =\; 100\; \backslash text\{\; cm\}$$

Since 100 cm is equal to 1 meter (1 m = 100 cm), the length of the tape required is 100 cm or 1 m.

Thus, the total length of tape required is 100 cm or 1 m.

First, we need to ensure that both the length and breadth are in the same unit. We will convert them to meters.

Length of the table top = 2 m 25 cm. Since 1 m = 100 cm, 25 cm = 0.25 m. So, Length = 2 m + 0.25 m = 2.25 m.

Breadth of the table top = 1 m 50 cm. Since 1 m = 100 cm, 50 cm = 0.50 m. So, Breadth = 1 m + 0.50 m = 1.50 m.

The formula for the perimeter of a rectangle is:

$$P\; =\; 2\; \backslash times\; (\backslash text\{length\}\; +\; \backslash text\{breadth\})$$

Substituting the values:

$$P\; =\; 2\; \backslash times\; (2.25\; \backslash text\{\; m\}\; +\; 1.50\; \backslash text\{\; m\})$$

$$P\; =\; 2\; \backslash times\; (3.75\; \backslash text\{\; m\})$$

$$P\; =\; 7.50\; \backslash text\{\; m\}$$

Thus, the perimeter of the table top is 7.50 m.

The length of the wooden strip required to frame the photograph is equal to the perimeter of the photograph.

Given: Length = 32 cm, Breadth = 21 cm.

The formula for the perimeter of a rectangle is:

$$P\; =\; 2\; \backslash times\; (\backslash text\{length\}\; +\; \backslash text\{breadth\})$$

Substituting the given values:

$$P\; =\; 2\; \backslash times\; (32\; \backslash text\{\; cm\}\; +\; 21\; \backslash text\{\; cm\})$$

$$P\; =\; 2\; \backslash times\; (53\; \backslash text\{\; cm\})$$

$$P\; =\; 106\; \backslash text\{\; cm\}$$

Thus, the length of the wooden strip required is 106 cm.