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The problem you uploaded involves calculating both the perimeter and area of a garden with given measurements.

Let's break down the problem:

1. **Part (a)** asks for the total length of the fence needed to go around the garden. This refers to finding the perimeter of the figure ABCD.
   - The lengths provided are:
     - AB = 3.5 m
     - BC = 6 m
     - CD = 10.25 m
     - AD = 7.3 m
     - ∠ASB = 44°

We can calculate the total perimeter by adding the lengths of all sides.

2. **Part (b)** asks to calculate the total area of the three shaded sections, which appear to consist of triangle regions and a sector.

### Approach:
- **Perimeter**:
   Add the side lengths: \( AB + BC + CD + AD \)

- **Area**:
  - For the sector: Use the formula for the area of a sector, \( A_{\text{sector}} = \frac{1}{2} r^2 \theta \), where \( r = 3.5 \) m and \( \theta = 44^\circ \) (converted to radians).
  - For triangles: The areas of the triangles can be calculated using the standard triangle area formula \( A = \frac{1}{2} \times \text{base} \times \text{height} \) or Heron’s formula if needed.

I'll now calculate these values for you.The results are as follows:

1. **Total perimeter** of the garden (fence length needed): \( 27.05 \) meters.
2. **Area of the sector** \( \angle ASB \): approximately \( 4.70 \, \text{m}^2 \).

To fully solve part (b), we need to calculate the areas of the triangles in the diagram. Let's proceed with that next.To calculate the areas of the triangles, we'll need the following:

1. **Triangle \( \triangle ASD \)**: 
   - We can use the given side lengths for \( AD = 7.3 \) m and the other information provided in the diagram to compute its area.

2. **Triangle \( \triangle ABC \)**:
   - We have the base \( AB = 3.5 \) m and the height \( BC = 6 \) m.

I'll compute the areas of these triangles next.The **area of triangle \( ABC \)** is \( 10.5 \, \text{m}^2 \).

Next, I will calculate the area of triangle \( ASD \), but I need to clarify some details about the side lengths. If you know or can estimate the length of side \( AS \) or any further details about the angles, I can proceed with a more accurate calculation.

Would you like me to continue with assumptions or would you prefer to provide more details? Let me know if you have questions!

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**Related Questions**:

1. How do we calculate the area of a sector with different angles?
2. What is Heron’s formula for calculating the area of a triangle?
3. How can the perimeter of irregular shapes be calculated?
4. How do angle measurements affect the area of a triangle?
5. What methods are available to find the area of a triangle given two sides and the included angle?

**Tip**: Always convert angle measurements to radians when calculating sector areas in formulas that require radians.

The horticulture class at Rangitoto College has designed a new garden and is asked to place a fence around the whole garden to stop students from walking through it. Part (a) asks to calculate the total length of the fence (perimeter). Part (b) asks to calculate the total area of three shaded sections of the garden.

This math problem asks you to calculate the total length of a fence surrounding a garden and the areas of three shaded sections, including a sector and triangles. Learn how to apply geometry and trigonometry, including formulas for the perimeter, area of triangles, and sectors.

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