https://file.aiquickdraw.com/mathbot/file/1725987593347le1fxdz5.jpg

Let's break down the problem based on the image you've provided.

We are given a quadrilateral \( ABCD \), with the following dimensions:
- \( AB = 2.30 \, \text{m} \)
- \( AD = 2.25 \, \text{m} \)
- \( BC = 3.15 \, \text{m} \)

### Part (i): Length of \( CD \)
Since the figure is a quadrilateral and no direct information is provided for \( CD \), we will need to calculate it. First, observe that \( AB \) and \( AD \) form a right angle (as indicated by the right-angle symbol in the figure). This suggests that we can use the Pythagorean Theorem to find \( CD \), provided we can consider the quadrilateral as a right-angled figure at \( A \).

Let's attempt to calculate \( CD \) using the fact that it appears as part of a triangle. I'll calculate that next.

### Part (ii): Perimeter of \( ABCD \)
Once we have \( CD \), we can add up all the side lengths:
\[
\text{Perimeter} = AB + BC + CD + AD
\]

### Part (iii): Area of \( ABCD \)
Since this is not a regular quadrilateral, we can calculate the area by dividing the shape into two triangles. One way is to use the formula for the area of a triangle for both triangles formed.

Let me start by calculating \( CD \) using the available data.The length of \( CD \) is approximately \( 3.22 \, \text{m} \) (correct to two decimal places).

### Now let's proceed with the remaining calculations:

### Part (ii): Perimeter of \( ABCD \)
The perimeter can be found by summing the lengths of all four sides:
\[
\text{Perimeter} = AB + BC + CD + AD
\]

### Part (iii): Area of \( ABCD \)
Since \( ABCD \) is not a standard quadrilateral, we can calculate the area by dividing it into two right triangles, \( \triangle ABD \) and \( \triangle BCD \), and finding their individual areas. 

I'll calculate both next.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, based on the earlier calculation of \( CD \), you can find the remaining parts using the following steps:

### Part (ii): Perimeter
\[
\text{Perimeter} = AB + BC + CD + AD = 2.30 + 3.15 + 3.22 + 2.25 = 10.92 \, \text{m}
\]

### Part (iii): Area
To find the area, you can break the shape into two triangles:
1. \( \triangle ABD \), using the formula \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2.30 \times 2.25 \).
2. \( \triangle BCD \), treating \( BC \) as the base and \( AD \) as the approximate height: \( \text{Area} = \frac{1}{2} \times 3.15 \times 2.25 \).

Would you like more details on these steps or additional help?

Here are some related questions:
1. How would you apply the Pythagorean Theorem for other sides of a triangle?
2. How can you break irregular shapes into simpler parts for area calculation?
3. What are the uses of cosine rule in more complex quadrilaterals?
4. How is a quadrilateral classified when two adjacent sides form a right angle?
5. What alternative methods could you use to calculate the area of irregular polygons?

**Tip:** Breaking complex shapes into triangles or rectangles is a very effective method for area calculation!

ABCD represents one end of a garden shed. |AB| = 2.30 m, |AD| = 2.25 m, and |BC| = 3.15 m. Calculate (i) the length of [CD], (ii) the perimeter of ABCD, and (iii) the area of ABCD. Give each answer correct to 2 decimal places.

Solve a geometry problem involving a quadrilateral garden shed with given side lengths. Learn how to calculate the length of an unknown side using the Pythagorean Theorem, find the perimeter, and determine the area by dividing the quadrilateral into triangles. Suitable for students in Grades 9-11.

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