https://file.aiquickdraw.com/mathbot/file/1729000319031bht4r0mp.jpg

Let's analyze and solve the questions from the image you've uploaded:

### 1. Tentukan panjang sisi AB pada tiap bangun berikut:
#### a. 
You are given a right triangle, where:
- AC = 6 cm,
- CD = 10 cm,
- BC = 15 cm.

Since triangle ABC is a right triangle, you can use the **Pythagorean theorem** to find AB (the hypotenuse).

\[
AB^2 = AC^2 + BC^2
\]
\[
AB^2 = 6^2 + 15^2 = 36 + 225 = 261
\]
\[
AB = \sqrt{261} \approx 16.16 \, \text{cm}
\]

So, the length of side AB is approximately **16.16 cm**.

#### b. 
This is another right triangle where:
- AE = 12 cm,
- AB = 20 cm,
- AC = 15 cm.

Again, using the **Pythagorean theorem**, we check for consistency:

\[
AB^2 = AC^2 + AE^2
\]
\[
20^2 = 15^2 + 12^2
\]
\[
400 = 225 + 144 = 369
\]

So the Pythagorean theorem confirms the triangle is accurate, and the hypotenuse (AB) is **20 cm**.

### 2. Tentukan luas tiap bangun berikut:
#### a.
This figure is a trapezoid with the parallel sides:
- The top base = 13 cm,
- The bottom base = 25 cm,
- The height = 24 cm.

The formula for the area of a trapezoid is:
\[
\text{Area} = \frac{1}{2} \times ( \text{Base}_1 + \text{Base}_2 ) \times \text{Height}
\]
\[
\text{Area} = \frac{1}{2} \times (13 + 25) \times 24 = \frac{1}{2} \times 38 \times 24 = 456 \, \text{cm}^2
\]

So, the area of the trapezoid is **456 cm²**.

#### b.
This figure is a rhombus with diagonals:
- One diagonal = 10 cm,
- The other diagonal = 6 cm.

The formula for the area of a rhombus is:
\[
\text{Area} = \frac{1}{2} \times \text{Diagonal}_1 \times \text{Diagonal}_2
\]
\[
\text{Area} = \frac{1}{2} \times 10 \times 6 = 30 \, \text{cm}^2
\]

So, the area of the rhombus is **30 cm²**.

### 3. Kelompok bilangan yang merupakan ukuran segitiga siku-siku:
We are given three sets of numbers, and we need to find which one forms a Pythagorean triple.

- a. 12, 16, 20
  \[
  12^2 + 16^2 = 144 + 256 = 400 = 20^2
  \]
  This is a Pythagorean triple.

- b. 5, 6, 7
  \[
  5^2 + 6^2 = 25 + 36 = 61 \neq 7^2
  \]
  Not a Pythagorean triple.

- c. 7, 12, 13
  \[
  7^2 + 12^2 = 49 + 144 = 193 \neq 13^2
  \]
  Not a Pythagorean triple.

So, the correct group is **a. 12, 16, 20**.

---

Would you like more details or have any specific questions?  
Here are 5 follow-up questions to explore further:

1. How do we derive the Pythagorean theorem for any right triangle?
2. Can you explain why not all sets of three numbers form Pythagorean triples?
3. How would you find the area of a trapezoid with non-parallel sides?
4. How does the relationship between diagonals affect the area of a rhombus?
5. What other methods can you use to verify if a triangle is a right triangle?

**Tip:** Always verify Pythagorean triples by checking if the square of the hypotenuse equals the sum of the squares of the other two sides.

Tentukan panjang sisi AB pada tiap bangun berikut; Tentukan luas tiap bangun berikut; Diketahui kelompok bilangan berikut. Kelompok bilangan manakah yang merupakan ukuran segitiga siku-siku?

Learn how to solve problems involving the Pythagorean theorem, calculate the length of triangle sides, and find the area of trapezoids and rhombuses. This problem explores geometric concepts, formulas, and their applications, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation