The diagram shows the floor of a room with dimensions 5m and 8m. Calculate (i) area (ii) perimeter.

The perimeter is the sum of all the lengths of the outer boundary.
The six segments are:

1. Top horizontal: $8 \text{ m}$
2. Right vertical (outer): $3 \text{ m}$
3. Bottom horizontal (outer): $5 \text{ m}$
4. Left vertical (outer): $5 \text{ m}$
5. Inner horizontal (step): $8 \text{ m} - 5 \text{ m} = 3 \text{ m}$
6. Inner vertical (step): $5 \text{ m} - 3 \text{ m} = 2 \text{ m}$

The perimeter of the shape is $\boxed{\text{26 m}}$.

We can split the L-shape into two rectangles in two ways, both should yield the same area.

Method 1: Split horizontally into a top rectangle and a bottom rectangle.

• Rectangle 1 (top part): Width $= 8 \text{ m}$ Height $= 5 \text{ m} - 3 \text{ m} = 2 \text{ m}$ (This is the height of the top section of the L-shape) Area 1 $= 8 \text{ m} \times 2 \text{ m} = 16 \text{ m}^2$.
• Rectangle 2 (bottom part): Width $= 5 \text{ m}$ (This is the length of the bottom horizontal segment) Height $= 3 \text{ m}$ (This is the height of the right vertical segment) Area 2 $= 5 \text{ m} \times 3 \text{ m} = 15 \text{ m}^2$.

Method 2: Split vertically into a left rectangle and a right rectangle.

• Rectangle A (left part): Width $= 8 \text{ m} - 5 \text{ m} = 3 \text{ m}$ (This is the width of the left section of the L-shape) Height $= 5 \text{ m}$ (This is the full height of the left side) Area A $= 3 \text{ m} \times 5 \text{ m} = 15 \text{ m}^2$.
• Rectangle B (right part): Width $= 5 \text{ m}$ (This is the length of the bottom horizontal segment) Height $= 3 \text{ m}$ (This is the height of the right vertical segment) Area B $= 5 \text{ m} \times 3 \text{ m} = 15 \text{ m}^2$.

There is a discrepancy between the two methods (31 m$^2$ vs 30 m$^2$). This indicates that the interpretation of the diagram's labels might be ambiguous or inconsistent.

Let's re-evaluate the diagram based on the most common convention for L-shaped figures, which is a large rectangle with a smaller rectangle cut out from one corner.
Assume the overall dimensions of the enclosing rectangle are $8 \text{ m}$ (width) and $5 \text{ m}$ (height).
The cut-out rectangle's dimensions are derived from the inner labels.
The inner horizontal segment is $5 \text{ m}$. This means the cut-out's width is $8 \text{ m} - 5 \text{ m} = 3 \text{ m}$.
The inner vertical segment is $3 \text{ m}$. This means the cut-out's height is $5 \text{ m} - 3 \text{ m} = 2 \text{ m}$.

So, the area of the large rectangle is $8 \text{ m} \times 5 \text{ m} = 40 \text{ m}^2$.
The area of the cut-out rectangle is $3 \text{ m} \times 2 \text{ m} = 6 \text{ m}^2$.
The area of the L-shape would then be $40 \text{ m}^2 - 6 \text{ m}^2 = 34 \text{ m}^2$.

However, the labels in the diagram are placed such that the $5 \text{ m}$ is the bottom horizontal length and the $3 \text{ m}$ is the right vertical length. This is the interpretation used in the first calculation attempt.

Let's stick to the interpretation where the $8 \text{ m}$ is the top length, $5 \text{ m}$ is the left height, $5 \text{ m}$ is the bottom length, and $3 \text{ m}$ is the right height.
The diagram is:

      8m
   +-----------------+
   |                 |
   |                 |
   |                 | 3m (Right vertical)
   +-----+-----------+
   |     |
   |     | 2m (Inner vertical, 5-3)
   |     |
   +-----+
     5m (Bottom horizontal)

For this specific shape:
Perimeter: $8 + 3 + 5 + (5-3) + (8-5) + 5 = 8 + 3 + 5 + 2 + 3 + 5 = 26 \text{ m}$. (This is consistent).

Area:
Let's use the method of splitting into two rectangles that is consistent with the labels.
Split into a top rectangle and a bottom rectangle:

• Top rectangle: width $8 \text{ m}$, height $(5 \text{ m} - 3 \text{ m}) = 2 \text{ m}$. Area $= 8 \text{ m} \times 2 \text{ m} = 16 \text{ m}^2$.
• Bottom rectangle: width $5 \text{ m}$, height $3 \text{ m}$. Area $= 5 \text{ m} \times 3 \text{ m} = 15 \text{ m}^2$. Total Area $= 16 \text{ m}^2 + 15 \text{ m}^2 = 31 \text{ m}^2$.

The discrepancy arises because if the overall width is $8 \text{ m}$ and the bottom segment is $5 \text{ m}$, then the inner horizontal segment must be $3 \text{ m}$. If the overall height is $5 \text{ m}$ and the right segment is $3 \text{ m}$, then the inner vertical segment must be $2 \text{ m}$.
The two methods of splitting the area should yield the same result. The fact that they don't implies an inconsistency in the diagram's labeling or my interpretation of how the labels define the shape.

Let's assume the most standard interpretation of an L-shape where the overall dimensions are given, and the inner dimensions define the "cut-out".
Overall width = $8 \text{ m}$
Overall height = $5 \text{ m}$
The inner horizontal line is $5 \text{ m}$. This means the cut-out is $8 \text{ m} - 5 \text{ m} = 3 \text{ m}$ wide.
The inner vertical line is $3 \text{ m}$. This means the cut-out is $5 \text{ m} - 3 \text{ m} = 2 \text{ m}$ high.

This means the shape is a $8 \text{ m} \times 5 \text{ m}$ rectangle with a $3 \text{ m} \times 2 \text{ m}$ rectangle cut out from one corner.
The perimeter of such a shape is always $2 \times (\text{overall width} + \text{overall height})$.
Perimeter $= 2 \times (8 \text{ m} + 5 \text{ m}) = 2 \times 13 \text{ m} = 26 \text{ m}$. This matches my perimeter calculation.

The area of such a shape is:
Area $= (\text{overall width} \times \text{overall height}) - (\text{cut-out width} \times \text{cut-out height})$
Area $= (8 \text{ m} \times 5 \text{ m}) - ((8 \text{ m} - 5 \text{ m}) \times (5 \text{ m} - 3 \text{ m}))$
Area $= 40 \text{ m}^2 - (3 \text{ m} \times 2 \text{ m})$
Area $= 40 \text{ m}^2 - 6 \text{ m}^2$
Area $= 34 \text{ m}^2$.

This method (subtracting the cut-out) is generally the most robust for L-shapes. The discrepancy in the splitting methods suggests that the labels $5 \text{ m}$ (bottom) and $3 \text{ m}$ (right) might be intended as the dimensions of the larger parts of the L-shape, not the inner steps.

Let's assume the diagram implies the following:

• The top horizontal length is $8 \text{ m}$.
• The left vertical length is $5 \text{ m}$.
• The bottom horizontal length is $5 \text{ m}$.
• The right vertical length is $3 \text{ m}$.

This is the interpretation I used for the perimeter calculation of $26 \text{ m}$.
For the area, I will use the subtraction method as it is less prone to misinterpretation of the split lines.

The overall dimensions of the enclosing rectangle are $8 \text{ m}$ (width) and $5 \text{ m}$ (height).
Area of the large rectangle $= 8 \text{ m} \times 5 \text{ m} = 40 \text{ m}^2$.

The dimensions of the cut-out (missing) rectangle are:
Width of cut-out $= 8 \text{ m} - 5 \text{ m} = 3 \text{ m}$
Height of cut-out $= 5 \text{ m} - 3 \text{ m} = 2 \text{ m}$
Area of cut-out rectangle $= 3 \text{ m} \times 2 \text{ m} = 6 \text{ m}^2$.

The area of the shape is $\boxed{\text{34 m}^2}$.