Let's solve this step-by-step.

Part (a): Scale Drawing

The given scale is 1:400, meaning that each 1 cm on the drawing represents 400 cm (or 4 meters) in real life. We’ll use this scale to calculate the dimensions for the drawing.

Given dimensions of the block:

• Height = 24 m
• Bottom side = 36 m
• Top side = 48 m

To find the scaled dimensions:

1. Height: $\frac{24 \text{ m}}{400} = 0.06 \text{ m} = 6 \text{ cm}$
2. Bottom side: $\frac{36 \text{ m}}{400} = 0.09 \text{ m} = 9 \text{ cm}$
3. Top side: $\frac{48 \text{ m}}{400} = 0.12 \text{ m} = 12 \text{ cm}$

In your scaled drawing, you should have:

• Height = 6 cm
• Bottom side = 9 cm
• Top side = 12 cm

Part (b): Perimeter

To find the perimeter of the block, sum the lengths of all sides. Since we need the length of the fourth side, which is diagonal, we can apply the Pythagorean theorem.

The fourth side forms a right triangle with the height (24 m) and the difference between the top and bottom sides $(48 \text{ m} - 36 \text{ m} = 12 \text{ m})$.

Using the Pythagorean theorem: $\text{Fourth side} = \sqrt{(24)^2 + (12)^2} = \sqrt{576 + 144} = \sqrt{720} \approx 26.83 \text{ m}$

Now, the perimeter is: $24 + 36 + 48 + 26.83 = 134.83 \approx 135 \text{ m (to the nearest meter)}$

Summary

1. Scale drawing dimensions: 6 cm, 9 cm, and 12 cm for height, bottom, and top sides respectively.
2. Perimeter: 135 m.

Would you like more details or have any questions?

Further Questions

1. How would the scale change if Toby wanted a 1:1000 drawing?
2. Can we use the same method to find the area of this shape?
3. How would changing the scale affect the perimeter in the drawing?
4. What other methods can be used to find the diagonal length in part (b)?
5. How do we round measurements in cases where accuracy is critical?

Tip: Always double-check your scaling calculations to ensure accuracy in technical drawings.