Math worksheet for Year 7/Grade 6 students covering perimeter, area, and volume calculations.

Let's solve each problem step by step.

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Problem 1: Perimeter of a square with a side of 3 cm

The formula for the perimeter of a square is:
\[
\text{Perimeter} = 4 \times \text{side length}
\]
Given that the side length is \(3 \, \text{cm}\):
\[
\text{Perimeter} = 4 \times 3 = 12 \, \text{cm}
\]

Answer:
\[
\boxed{d \, 12 \, \text{cm}}
\]

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Problem 2: Area of a square with a side of 4 cm

The formula for the area of a square is:
\[
\text{Area} = \text{side length}^2
\]
Given that the side length is \(4 \, \text{cm}\):
\[
\text{Area} = 4^2 = 16 \, \text{cm}^2
\]

Answer:
\[
\boxed{a \, 16 \, \text{cm}^2}
\]

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Problem 3: Perimeter of the given shape

The shape is a rectangle with dimensions \(8 \, \text{cm}\) (length) and \(3 \, \text{cm}\) (height), but it has an additional segment of \(3 \, \text{cm}\) extending from one side. To find the perimeter, we need to sum all the outer edges.

The shape can be broken down as follows:
- Two vertical sides: \(3 \, \text{cm}\) each
- One horizontal side at the top: \(8 \, \text{cm}\)
- One horizontal side at the bottom: \(8 \, \text{cm}\)
- An additional horizontal segment: \(3 \, \text{cm}\)

Now, calculate the total perimeter:
\[
\text{Perimeter} = 3 + 3 + 8 + 8 + 3 = 25 \, \text{cm}
\]

However, upon re-examining the diagram, it appears there might be a misunderstanding in the interpretation. The shape seems to be a single rectangle with dimensions \(8 \, \text{cm}\) by \(3 \, \text{cm}\). Let's recalculate assuming this simpler interpretation:

For a rectangle:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width}) = 2 \times (8 + 3) = 2 \times 11 = 22 \, \text{cm}
\]

Answer:
\[
\boxed{b \, 22 \, \text{cm}}
\]

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Problem 4: Length of an edge of a cube with a volume of \(64 \, \text{cm}^3\)

The formula for the volume of a cube is:
\[
\text{Volume} = \text{edge length}^3
\]
Given that the volume is \(64 \, \text{cm}^3\), let the edge length be \(x\):
\[
x^3 = 64
\]
To find \(x\), take the cube root of both sides:
\[
x = \sqrt[3]{64} = 4 \, \text{cm}
\]

Answer:
\[
\boxed{d \, 4 \, \text{cm}}
\]

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Final Answers:

1. \(\boxed{d \, 12 \, \text{cm}}\)
2. \(\boxed{a \, 16 \, \text{cm}^2}\)
3. \(\boxed{b \, 22 \, \text{cm}}\)
4. \(\boxed{d \, 4 \, \text{cm}}\)