Solved Volume of: Pyramids, Cones, Prisms, ka Cylinders Maze ... - Free Printable

To find the correct path through the maze, we need to calculate the surface area of the shape in the highlighted yellow box and see which number matches it.

Step 1: Identify the shape and its dimensions.
The shape in the yellow box is a square pyramid. This means it has a square base and four triangular faces that meet at a point at the top.
From the diagram, we can see:
* The side length of the square base ($s$) is 8 m.
* The slant height of the triangular faces ($l$) is 9 m. (This is the height of the triangle from the base to the tip, not the vertical height of the pyramid).

Step 2: Calculate the area of the base.
The base is a square.
$$ \text{Area of Base} = \text{side} \times \text{side} $$
$$ \text{Area of Base} = 8 \, \text{m} \times 8 \, \text{m} = 64 \, \text{m}^2 $$

Step 3: Calculate the area of the four triangular faces (Lateral Area).
Each face is a triangle with a base of 8 m and a height (slant height) of 9 m.
$$ \text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} $$
$$ \text{Area of one triangle} = \frac{1}{2} \times 8 \, \text{m} \times 9 \, \text{m} $$
$$ \text{Area of one triangle} = 4 \, \text{m} \times 9 \, \text{m} = 36 \, \text{m}^2 $$

Since there are 4 identical triangular faces:
$$ \text{Total Lateral Area} = 4 \times 36 \, \text{m}^2 = 144 \, \text{m}^2 $$

Step 4: Calculate the Total Surface Area.
Add the area of the base and the total lateral area together.
$$ \text{Total Surface Area} = \text{Area of Base} + \text{Total Lateral Area} $$
$$ \text{Total Surface Area} = 64 \, \text{m}^2 + 144 \, \text{m}^2 $$
$$ \text{Total Surface Area} = 208 \, \text{m}^2 $$

Conclusion:
The calculated surface area is 208 m². Looking at the arrows connected to the yellow box, the arrow pointing down leads to a box labeled 208 m², which confirms our calculation is the correct key to unlock the next part of the maze.

Final Answer:
208 m²