CBSE Class 7 Mathematics Chapter 11: Perimeter and Area NCERT Solutions

Given the dimensions of the rectangular piece of land:

• Length = 500 m
• Breadth = 300 m

1. To find the area of the rectangular piece of land:

The formula for the area of a rectangle is Length × Breadth.

$$Area\; =\; 500\; \backslash text\{\; m\}\; \backslash times\; 300\; \backslash text\{\; m\}$$

$$Area\; =\; 1,50,000\; \backslash text\{\; m\}^2$$

So, the area of the land is 1,50,000 square meters.

2. To find the cost of the land:

We are given that the cost of 1 square meter of land is ₹10,000.

To find the total cost, we multiply the total area by the cost per square meter.

$$Total\; Cost\; =\; Area\; \backslash times\; \backslash text\{Cost\; per\; m\}^2$$

$$Total\; Cost\; =\; 1,50,000\; \backslash text\{\; m\}^2\; \backslash times\; \backslash text\{₹\}10,000\; /\; \backslash text\{m\}^2$$

$$Total\; Cost\; =\; \backslash text\{₹\}1,50,00,00,000$$

Therefore, the cost of the land is ₹1,50,00,00,000 (one hundred fifty crore rupees).

Given the perimeter of the square park = 320 m.

The formula for the perimeter of a square is 4 × side.

$$4\; \backslash times\; \backslash text\{side\}\; =\; 320\; \backslash text\{\; m\}$$

To find the length of one side, we divide the perimeter by 4:

$$\backslash text\{side\}\; =\; \backslash frac\{320\; \backslash text\{\; m\}\}\{4\}$$

$$\backslash text\{side\}\; =\; 80\; \backslash text\{\; m\}$$

Now, we can find the area of the square park. The formula for the area of a square is side × side.

$$Area\; =\; \backslash text\{side\}\; \backslash times\; \backslash text\{side\}$$

$$Area\; =\; 80\; \backslash text\{\; m\}\; \backslash times\; 80\; \backslash text\{\; m\}$$

$$Area\; =\; 6400\; \backslash text\{\; m\}^2$$

Thus, the area of the square park is 6400 square meters.

Given the area of the rectangular plot = 440 m² and the length = 22 m.

The formula for the area of a rectangle is Length × Breadth.

$$Area\; =\; \backslash text\{Length\}\; \backslash times\; \backslash text\{Breadth\}$$

$$440\; \backslash text\{\; m\}^2\; =\; 22\; \backslash text\{\; m\}\; \backslash times\; \backslash text\{Breadth\}$$

To find the breadth, we rearrange the formula:

$$\backslash text\{Breadth\}\; =\; \backslash frac\{\backslash text\{Area\}\}\{\backslash text\{Length\}\}$$

$$\backslash text\{Breadth\}\; =\; \backslash frac\{440\; \backslash text\{\; m\}^2\}\{22\; \backslash text\{\; m\}\}$$

$$\backslash text\{Breadth\}\; =\; 20\; \backslash text\{\; m\}$$

So, the breadth of the rectangular plot is 20 meters.

Now, we need to find the perimeter of the rectangular plot.

The formula for the perimeter of a rectangle is 2 × (Length + Breadth).

$$Perimeter\; =\; 2\; \backslash times\; (\backslash text\{Length\}\; +\; \backslash text\{Breadth\})$$

$$Perimeter\; =\; 2\; \backslash times\; (22\; \backslash text\{\; m\}\; +\; 20\; \backslash text\{\; m\})$$

$$Perimeter\; =\; 2\; \backslash times\; (42\; \backslash text\{\; m\})$$

$$Perimeter\; =\; 84\; \backslash text\{\; m\}$$

Thus, the breadth of the rectangular plot is 20 m and its perimeter is 84 m.

Given the perimeter of the rectangular sheet = 100 cm and the length = 35 cm.

The formula for the perimeter of a rectangle is 2 × (Length + Breadth).

$$2\; \backslash times\; (\backslash text\{Length\}\; +\; \backslash text\{Breadth\})\; =\; 100\; \backslash text\{\; cm\}$$

Substitute the given length into the formula:

$$2\; \backslash times\; (35\; \backslash text\{\; cm\}\; +\; \backslash text\{Breadth\})\; =\; 100\; \backslash text\{\; cm\}$$

Divide both sides by 2:

$$35\; \backslash text\{\; cm\}\; +\; \backslash text\{Breadth\}\; =\; \backslash frac\{100\; \backslash text\{\; cm\}\}\{2\}$$

$$35\; \backslash text\{\; cm\}\; +\; \backslash text\{Breadth\}\; =\; 50\; \backslash text\{\; cm\}$$

To find the breadth, subtract the length from 50 cm:

$$\backslash text\{Breadth\}\; =\; 50\; \backslash text\{\; cm\}\; -\; 35\; \backslash text\{\; cm\}$$

$$\backslash text\{Breadth\}\; =\; 15\; \backslash text\{\; cm\}$$

So, the breadth of the rectangular sheet is 15 cm.

Now, we need to find the area of the rectangular sheet. The formula for the area of a rectangle is Length × Breadth.

$$Area\; =\; \backslash text\{Length\}\; \backslash times\; \backslash text\{Breadth\}$$

$$Area\; =\; 35\; \backslash text\{\; cm\}\; \backslash times\; 15\; \backslash text\{\; cm\}$$

$$Area\; =\; 525\; \backslash text\{\; cm\}^2$$

Thus, the breadth of the rectangular sheet is 15 cm and its area is 525 cm².

Given:

• Side of the square park = 60 m
• Length of the rectangular park = 90 m

According to the problem, the area of the square park is equal to the area of the rectangular park.

First, calculate the area of the square park:

$$Area\; of\; Square\; =\; side\; \backslash times\; side$$

$$Area\; of\; Square\; =\; 60\; \backslash text\{\; m\}\; \backslash times\; 60\; \backslash text\{\; m\}$$

$$Area\; of\; Square\; =\; 3600\; \backslash text\{\; m\}^2$$

Since the area of the rectangular park is the same as the area of the square park:

$$Area\; of\; Rectangle\; =\; 3600\; \backslash text\{\; m\}^2$$

The formula for the area of a rectangle is Length × Breadth.

$$Area\; of\; Rectangle\; =\; \backslash text\{Length\}\; \backslash times\; \backslash text\{Breadth\}$$

$$3600\; \backslash text\{\; m\}^2\; =\; 90\; \backslash text\{\; m\}\; \backslash times\; \backslash text\{Breadth\}$$

To find the breadth of the rectangular park, we rearrange the formula:

$$\backslash text\{Breadth\}\; =\; \backslash frac\{\backslash text\{Area\; of\; Rectangle\}\}\{\backslash text\{Length\}\}$$

$$\backslash text\{Breadth\}\; =\; \backslash frac\{3600\; \backslash text\{\; m\}^2\}\{90\; \backslash text\{\; m\}\}$$

$$\backslash text\{Breadth\}\; =\; 40\; \backslash text\{\; m\}$$

Thus, the breadth of the rectangular park is 40 meters.