https://file.aiquickdraw.com/mathbot/file/1725933774105h8fco4zd.jpg

Let's solve each part of the problem based on the provided diagrams.

### a. Determine the length of side \( AB \)

In the first diagram (a), we have a trapezoid, and we need to find side \( AB \). The given information is:
- \( CD = 10 \, \text{cm} \) (height)
- \( AD = 6 \, \text{cm} \) (one side of the right triangle at \( A \))
- \( BC = 15 \, \text{cm} \) (upper base of the trapezoid)

Looking at the right triangle \( \triangle ABC \), where \( AC \) is the hypotenuse:
- \( AB \) can be found using the Pythagorean theorem.

\[
AB^2 = BC^2 + CD^2
\]

Substituting the values:

\[
AB^2 = 15^2 + 10^2
\]
\[
AB^2 = 225 + 100 = 325
\]
\[
AB = \sqrt{325} \approx 18.03 \, \text{cm}
\]

So, the length of side \( AB \) is approximately \( 18.03 \, \text{cm} \).

---

### b. Determine the length of side \( AB \)

In the second diagram (b), we have a triangle, and we need to find side \( AB \). The given information is:
- \( AC = 15 \, \text{cm} \) (one side of the triangle)
- \( BC = 20 \, \text{cm} \) (another side of the triangle)
- \( CE = 12 \, \text{cm} \) (height of the triangle from vertex \( C \))

To find \( AB \), we use the fact that it's a right triangle \( \triangle AEB \). Again, applying the Pythagorean theorem:

\[
AB^2 = AC^2 + BC^2
\]

Substituting the values:

\[
AB^2 = 15^2 + 20^2 = 225 + 400 = 625
\]
\[
AB = \sqrt{625} = 25 \, \text{cm}
\]

So, the length of side \( AB \) is \( 25 \, \text{cm} \).

---

Would you like further clarification on any of these steps or more details?

### Related questions:
1. How is the Pythagorean theorem used to calculate the sides of a triangle?
2. Can the Pythagorean theorem be used in non-right triangles?
3. What are the properties of trapezoids that help in solving geometric problems?
4. How do you calculate the area of a trapezoid or a triangle?
5. What other methods can be used to solve for unknown sides in geometric shapes?

**Tip:** When solving problems with right triangles, always check if you can apply the Pythagorean theorem for efficient calculation!

Tentukan panjang sisi AB pada tiap bangun berikut (image with two geometric shapes).

Find the length of side AB in right-angle triangles based on the given side lengths using the Pythagorean theorem. For trapezoids and triangles, this problem involves calculating unknown sides with height and base information. Suitable for students in Grades 9-10.

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