CBSE Class 7 Mental Maths Perimeter And Area Worksheet - Free Printable

Let's solve each question from Chapter 11: Perimeter and Area step by step, using the formulas provided.

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Question 1:

One of the sides and the corresponding height of a parallelogram are 5 cm and 3 cm respectively. Find the area of the parallelogram.

Solution:
We know:
> Area of a Parallelogram = base × corresponding height

Given:
- Base = 5 cm
- Height = 3 cm

So,
$$
\text{Area} = 5 \times 3 = 15 \text{ cm}^2
$$

✔ Answer: $ \boxed{15} \text{ cm}^2 $

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Question 2:

In a triangle, if one side is 7 cm and its corresponding height is 4 cm, find its area.

Solution:
> Area of a Triangle = $ \frac{1}{2} \times \text{base} \times \text{height} $

Given:
- Base = 7 cm
- Height = 4 cm

$$
\text{Area} = \frac{1}{2} \times 7 \times 4 = \frac{1}{2} \times 28 = 14 \text{ cm}^2
$$

✔ Answer: $ \boxed{14} \text{ cm}^2 $

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Question 3:

If area of ΔABC is 49 cm² and its height AD is 7 cm, find BC.

Solution:
Here, AD is the height from A to side BC (so BC is the base).

> Area = $ \frac{1}{2} \times \text{base} \times \text{height} $

Given:
- Area = 49 cm²
- Height (AD) = 7 cm
- Let BC = $ x $ cm

$$
49 = \frac{1}{2} \times x \times 7
$$
$$
49 = \frac{7x}{2}
$$
Multiply both sides by 2:
$$
98 = 7x \Rightarrow x = \frac{98}{7} = 14
$$

✔ Answer: $ \boxed{14} \text{ cm} $

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Question 4:

If area of a parallelogram is 17.6 cm² and its base is 4 cm, find its corresponding height.

Solution:
> Area = base × height

Given:
- Area = 17.6 cm²
- Base = 4 cm

Let height = $ h $

$$
17.6 = 4 \times h \Rightarrow h = \frac{17.6}{4} = 4.4 \text{ cm}
$$

✔ Answer: $ \boxed{4.4} \text{ cm} $

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Question 5:

Find the breadth of a rectangular plot if its area is 440 cm² and length is 22 cm. Also find its perimeter.

Solution:
> Area of rectangle = length × breadth

Given:
- Area = 440 cm²
- Length = 22 cm

Let breadth = $ b $

$$
440 = 22 \times b \Rightarrow b = \frac{440}{22} = 20 \text{ cm}
$$

Now, perimeter:
> Perimeter = $ 2(\text{length} + \text{breadth}) = 2(22 + 20) = 2 \times 42 = 84 \text{ cm} $

✔ Answer:
- Breadth = $ \boxed{20} \text{ cm} $
- Perimeter = $ \boxed{84} \text{ cm} $

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Question 6:

The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth.

Solution:
> Perimeter = $ 2(\text{length} + \text{breadth}) $

Given:
- Perimeter = 100 cm
- Length = 35 cm
- Let breadth = $ b $

$$
100 = 2(35 + b)
\Rightarrow 50 = 35 + b
\Rightarrow b = 50 - 35 = 15 \text{ cm}
$$

✔ Answer: $ \boxed{15} \text{ cm} $

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Question 7:

The length and breadth of a rectangular plot are in the ratio of 4 : 3. If the perimeter is 140 cm, find its area.

Solution:
Let:
- Length = $ 4x $
- Breadth = $ 3x $

Perimeter = $ 2(\text{length} + \text{breadth}) = 2(4x + 3x) = 2(7x) = 14x $

Given:
- Perimeter = 140 cm

$$
14x = 140 \Rightarrow x = 10
$$

So:
- Length = $ 4x = 40 $ cm
- Breadth = $ 3x = 30 $ cm

Now, Area = $ \text{length} \times \text{breadth} = 40 \times 30 = 1200 \text{ cm}^2 $

✔ Answer: $ \boxed{1200} \text{ cm}^2 $

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Question 8:

The length and breadth of a rectangular park are in ratio 9 : 5. If its perimeter is 280 m, find its area.

Solution:
Let:
- Length = $ 9x $
- Breadth = $ 5x $

Perimeter = $ 2(9x + 5x) = 2(14x) = 28x $

Given:
- Perimeter = 280 m

$$
28x = 280 \Rightarrow x = 10
$$

So:
- Length = $ 9x = 90 $ m
- Breadth = $ 5x = 50 $ m

Area = $ 90 \times 50 = 4500 \text{ m}^2 $

✔ Answer: $ \boxed{4500} \text{ m}^2 $

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✔ Final Answers Summary:

| Question | Answer |
|--------|--------|
| 1 | 15 cm² |
| 2 | 14 cm² |
| 3 | 14 cm |
| 4 | 4.4 cm |
| 5 | Breadth = 20 cm, Perimeter = 84 cm |
| 6 | 15 cm |
| 7 | 1200 cm² |
| 8 | 4500 m² |

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