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The problem states:

"A right-angled trapezoid has a height of \( 4\sqrt{3} \, \text{cm} \). One of its parallel sides measures \( 7\sqrt{3} \, \text{cm} \), and its slanted side is \( 5\sqrt{3} \, \text{cm} \). Determine the perimeter of the trapezoid."

### Step-by-step solution:

1. **Trapezoid Properties**:
   - A right-angled trapezoid has two parallel sides (let's call them \( a \) and \( b \)), and two non-parallel sides: the height \( h \) and a slanted side (hypotenuse).

2. **Given Values**:
   - Height \( h = 4\sqrt{3} \, \text{cm} \).
   - One parallel side \( a = 7\sqrt{3} \, \text{cm} \).
   - Slanted side (hypotenuse) \( c = 5\sqrt{3} \, \text{cm} \).

3. **Calculating the Second Parallel Side**:
   - Since the trapezoid is right-angled, the other side (the shorter base, \( b \)) can be calculated using the Pythagorean theorem, where the height \( h \), the shorter base \( b \), and the slanted side \( c \) form a right triangle.
   
   Using the Pythagorean theorem:
   \[
   c^2 = h^2 + b^2
   \]
   Substituting the known values:
   \[
   (5\sqrt{3})^2 = (4\sqrt{3})^2 + b^2
   \]
   Simplifying:
   \[
   75 = 48 + b^2
   \]
   \[
   b^2 = 75 - 48 = 27
   \]
   \[
   b = \sqrt{27} = 3\sqrt{3} \, \text{cm}
   \]

4. **Calculating the Perimeter**:
   The perimeter \( P \) of the trapezoid is the sum of all four sides:
   \[
   P = a + b + h + c
   \]
   Substituting the known values:
   \[
   P = 7\sqrt{3} + 3\sqrt{3} + 4\sqrt{3} + 5\sqrt{3}
   \]
   Simplifying:
   \[
   P = (7 + 3 + 4 + 5)\sqrt{3} = 19\sqrt{3} \, \text{cm}
   \]

Thus, the perimeter of the trapezoid is \( 19\sqrt{3} \, \text{cm} \).

Would you like any further explanation?

### Related questions:
1. How would the solution change if the trapezoid wasn't right-angled?
2. Can the Pythagorean theorem be applied to all trapezoids?
3. How do we derive the area of this trapezoid?
4. What is the relationship between the height and the area of a trapezoid?
5. How can trigonometry be used to solve similar trapezoid problems?

### Tip:
Remember, the Pythagorean theorem is only applicable in right-angled triangles or figures containing them, like this trapezoid.

Suatu trapesium siku-siku mempunyai tinggi 4√3 cm. Diketahui salah satu sisi sejajarnya 7√3 cm dan sisi miringnya 5√3 cm. Tentukan keliling trapesium tersebut.

Learn how to calculate the perimeter of a right-angled trapezoid with a height of 4√3 cm, one parallel side of 7√3 cm, and a slanted side of 5√3 cm. This problem involves the Pythagorean theorem and perimeter calculation, suitable for students in Grades 8-10.

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