Worksheet on Area of a Square and Rectangle | Area of Squares & Rectan - Free Printable

Let's solve each part of the problem step by step using the formulas for perimeter and area:

🔷 Formulas:

- Rectangle:
- Perimeter = $ 2 \times (Length + Breadth) $
- Area = $ Length \times Breadth $
- Square:
- Perimeter = $ 4 \times Side $
- Area = $ Side^2 $

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We'll fill in the missing values in the table.

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(i) Rectangle

Given:
- Breadth = 16 m
- Area = 320 sq. m

We need to find Length and Perimeter.

#### Step 1: Find Length
$$
\text{Area} = \text{Length} \times \text{Breadth}
\Rightarrow 320 = \text{Length} \times 16
\Rightarrow \text{Length} = \frac{320}{16} = 20 \, \text{m}
$$

#### Step 2: Find Perimeter
$$
\text{Perimeter} = 2 \times (Length + Breadth) = 2 \times (20 + 16) = 2 \times 36 = 72 \, \text{m}
$$

✔ So:
- Length = 20 m
- Perimeter = 72 m

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(ii) Rectangle

Given:
- Length = 28 cm
- Perimeter = 70 cm

Find Breadth and Area

#### Step 1: Use Perimeter formula
$$
\text{Perimeter} = 2 \times (Length + Breadth)
\Rightarrow 70 = 2 \times (28 + Breadth)
\Rightarrow 35 = 28 + Breadth
\Rightarrow Breadth = 35 - 28 = 7 \, \text{cm}
$$

#### Step 2: Find Area
$$
\text{Area} = Length \times Breadth = 28 \times 7 = 196 \, \text{sq. cm}
$$

✔ So:
- Breadth = 7 cm
- Area = 196 sq. cm

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(iii) Square

Given:
- Perimeter = 84 m

Find Side, Area

#### Step 1: Find Side
$$
\text{Perimeter} = 4 \times \text{Side}
\Rightarrow 84 = 4 \times \text{Side}
\Rightarrow \text{Side} = \frac{84}{4} = 21 \, \text{m}
$$

#### Step 2: Find Area
$$
\text{Area} = \text{Side}^2 = 21^2 = 441 \, \text{sq. m}
$$

✔ So:
- Side = 21 m (Length = Breadth = 21 m)
- Area = 441 sq. m

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(iv) Rectangle

Given:
- Length = 50 mm
- Breadth = 20 mm
- Area = 1000 sq. mm

Check if area matches:
$$
\text{Area} = 50 \times 20 = 1000 \, \text{sq. mm} \quad \text{✓ Correct}
$$

Now find Perimeter:
$$
\text{Perimeter} = 2 \times (50 + 20) = 2 \times 70 = 140 \, \text{mm}
$$

✔ So:
- Perimeter = 140 mm

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(v) Square

Given:
- Side = 4 mm
- Area = 16 sq. cm → ✘ Wait! Units don't match!

Let’s check:
- Area of square with side 4 mm:
$$
\text{Area} = 4^2 = 16 \, \text{sq. mm}
$$
But the given area is 16 sq. cm, which is not equal to 16 sq. mm.

So there’s a unit inconsistency here.

Let’s resolve it:

We are told:
- Side = 4 mm
- Area = 16 sq. cm

But:
- 1 cm = 10 mm → 1 sq. cm = 100 sq. mm
- So 16 sq. cm = 1600 sq. mm

But area of 4 mm × 4 mm = 16 sq. mm ≠ 1600 sq. mm

So either:
- The side is not 4 mm, or
- The area is not 16 sq. cm

But let’s suppose the area is 16 sq. mm, then:
- Side = √16 = 4 mm → ✔ Matches

Alternatively, if area is 16 sq. cm, then:
- Side = √16 = 4 cm → So side should be 4 cm, not 4 mm

But in the table, it says side = 4 mm, so likely a typo in units.

Let’s assume the area is 16 sq. mm (since 4 mm × 4 mm = 16 sq. mm), and the "sq. cm" is a mistake.

But the table says 16 sq. cm, so let's recheck.

Wait — perhaps the side is 4 cm, not 4 mm?

Let’s suppose the side is 4 cm, then:
- Area = 4² = 16 sq. cm → ✔ Matches

So likely, "4 mm" is a typo, and it should be 4 cm.

But as per table: Side = 4 mm, Area = 16 sq. cm → This is inconsistent.

Let’s calculate what side would give 16 sq. cm:
$$
\text{Side} = \sqrt{16} = 4 \, \text{cm}
$$

So:
- If area is 16 sq. cm → side must be 4 cm
- But table says side is 4 mm → That’s 0.4 cm → area = (0.4)^2 = 0.16 sq. cm ≠ 16

So the only way both can be true is if the unit of side is wrong.

✔ Conclusion: The side should be 4 cm, not 4 mm.

But since the table says 4 mm, and 16 sq. cm, we must consider this as an error.

Alternatively, maybe the area is 16 sq. mm?

Then:
- Side = √16 = 4 mm → ✔ Matches

So likely, "16 sq. cm" is a typo, and it should be 16 sq. mm

We’ll proceed assuming that.

So:
- Side = 4 mm
- Area = 16 sq. mm
- Perimeter = 4 × 4 = 16 mm

✔ So:
- Perimeter = 16 mm
- Area = 16 sq. mm (not sq. cm)

But since the table says 16 sq. cm, and that doesn’t match, we must correct it.

Final Decision:

Assuming the side is 4 cm, then:
- Area = 16 sq. cm → ✔
- Perimeter = 4 × 4 = 16 cm

So probably, the "4 mm" is a typo, and it should be 4 cm

Or, if it's really 4 mm, then area is 16 sq. mm, not sq. cm.

But since the table says 16 sq. cm, we go with:
- Side = 4 cm
- Area = 16 sq. cm
- Perimeter = 16 cm

So likely, "4 mm" should be "4 cm"

We’ll update accordingly.

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✔ Final Completed Table:

| S.No. | Shape | Length | Breadth | Perimeter | Area |
|-------|-----------|------------|-----------|------------------|----------------|
| (i) | Rectangle | 20 m | 16 m | 72 m | 320 sq. m |
| (ii) | Rectangle | 28 cm | 7 cm | 70 cm | 196 sq. cm |
| (iii) | Square | 21 m | 21 m | 84 m | 441 sq. m |
| (iv) | Rectangle | 50 mm | 20 mm | 140 mm | 1000 sq. mm |
| (v) | Square | 4 cm | 4 cm | 16 cm | 16 sq. cm |

> 🛠️ Note: In (v), the original entry had 4 mm, but that leads to contradiction. We corrected it to 4 cm to match area = 16 sq. cm.

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✔ Summary of Answers:

1. (i)
- Length = 20 m
- Perimeter = 72 m

2. (ii)
- Breadth = 7 cm
- Area = 196 sq. cm

3. (iii)
- Side = 21 m
- Area = 441 sq. m

4. (iv)
- Perimeter = 140 mm

5. (v)
- Side = 4 cm (corrected from 4 mm)
- Perimeter = 16 cm

Let me know if you want the corrected version of the image or explanation in another format!