https://file.aiquickdraw.com/mathbot/file/1728723438753lvz7yrzn.jpg

Let’s extract the given information and solve the problem:

### **Given:**
- Trapezium \(ABCD\), with \(AB\) perpendicular to \(BC\).
- \(AB = 3 \, \text{cm}\)
- \(BC = 5 \, \text{cm}\)
- \(CD = 5 \, \text{cm}\)
- \(AD > 6 \, \text{cm}\)

### **To Find:**
- The **perimeter** of the trapezium, expressed as an integer.

---

### **Understanding the Problem:**
1. We need to find the perimeter of the trapezium, which is the sum of all side lengths:
   \[
   \text{Perimeter} = AB + BC + CD + AD
   \]
2. Since \(AB = 3 \, \text{cm}\), \(BC = 5 \, \text{cm}\), and \(CD = 5 \, \text{cm}\), we need the length of \(AD\). 

3. It is given that \(AD > 6 \, \text{cm}\). This means the smallest possible integer value for \(AD\) would be 7 cm.

---

### **Calculation:**
Using \(AD = 7 \, \text{cm}\) (since it must be greater than 6 cm):
\[
\text{Perimeter} = AB + BC + CD + AD = 3 + 5 + 5 + 7 = 20 \, \text{cm}
\]

---

### **Final Answer:**
The perimeter of the trapezium is:
\[
\boxed{20} \, \text{cm}
\]

---

Let me know if you have questions or want further details!

---

Here are some related questions to explore:
1. How do you calculate the area of a trapezium?
2. What happens if \(AB\) and \(CD\) are parallel in a trapezium?
3. How do you apply the Pythagorean theorem to trapeziums?
4. What are the properties of a right-angled trapezium?
5. How would the perimeter change if \(AD\) were a diagonal instead of a side?

**Tip:** Always check if the sides fit the geometric constraints when given inequalities, like \(AD > 6\).

In a trapezium ABCD, AB is perpendicular to BC. If AB = 3 cm, BC = 5 cm, CD = 5 cm and AD > 6 cm, then the perimeter of the trapezium, in cm, is ______.

Solve for the perimeter of trapezium ABCD where AB = 3 cm, BC = 5 cm, CD = 5 cm, and AD is greater than 6 cm. Learn how to apply the perimeter formula to find the solution, suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation