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The question asks us to find the perimeter of a right-angled trapezoid, given the height, one parallel side, and the slant side. The dimensions provided are:

- Height (\( h \)): \( 4\sqrt{3} \) cm
- One parallel side (\( a \)): \( 7\sqrt{3} \) cm
- Slant side (\( c \)): \( 5\sqrt{3} \) cm

To find the perimeter, we need to determine the length of the other parallel side (\( b \)) and the length of the other perpendicular side (\( d \)).

Using the Pythagorean theorem for the right triangle formed by the height, slant side, and the difference between the two parallel sides, we have:

\[
(h)^2 + (b - a)^2 = (c)^2
\]

Substituting the given values:

\[
(4\sqrt{3})^2 + (b - 7\sqrt{3})^2 = (5\sqrt{3})^2
\]

Calculating this will provide the length of \( b \), and then the perimeter can be calculated by adding up all the side lengths. Let's calculate \( b \) first.The solutions for \( b \) are \( 4\sqrt{3} \) cm and \( 10\sqrt{3} \) cm. Given that \( b \) must be different from \( a \) (which is \( 7\sqrt{3} \) cm), we can use \( b = 10\sqrt{3} \) cm.

Now, to find the perimeter, we'll add up all the side lengths:

- Side \( a \): \( 7\sqrt{3} \) cm
- Side \( b \): \( 10\sqrt{3} \) cm
- Height \( d \) (perpendicular side): \( 4\sqrt{3} \) cm (same as the height)
- Slant side \( c \): \( 5\sqrt{3} \) cm

Let's compute the perimeter.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you have any other questions or need assistance with a different topic, feel free to ask! Here are some related questions you might consider:

1. How can you determine the area of a right-angled trapezoid given similar dimensions?
2. What is the significance of the Pythagorean theorem in solving problems related to right triangles?
3. Can you explain how to calculate the length of the other perpendicular side of a trapezoid if the angles are known?
4. What are other properties of trapezoids that can be interesting to study?
5. How does the concept of similarity apply to trapezoids?

**Tip:** When working with right-angled figures, always consider the Pythagorean theorem as a useful tool for finding missing dimensions.

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.

Discover how to calculate the perimeter of a right-angled trapezoid with heights of 4√3 cm, one parallel side of 7√3 cm, and a slant side of 5√3 cm using the Pythagorean Theorem. This geometry problem is suitable for students in grades 9-10.

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