# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-7/4

Exercises: Try Out - Set 7: Real exam simulation to sharpen your skills and build confidence. - Question 4

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## Exercise 4

### Question

export const metadata = {
  title: "Question 4",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/24/2025",
};

Given the following <InlineMath math="4" /> plane figures:

1. Right trapezoid.
2. Regular pentagon.
3. Equilateral triangle.
4. Kite (not a square).

How many of these plane figures have at most <InlineMath math="2" /> lines of symmetry and <InlineMath math="2" /> rotational symmetries?


### Choices

- [ ] $$0$$
- [ ] $$1$$
- [x] $$2$$
- [ ] $$3$$
- [ ] $$4$$

### Answer & Explanation

export const metadata = {
  title: "Question 4 Explanation",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/24/2025",
};

We will analyze the number of lines of symmetry and rotational symmetries for each plane figure. The requirement is to have **at most** <InlineMath math="2" /> lines of symmetry **and** <InlineMath math="2" /> rotational symmetries.

#### Analyzing Right Trapezoid

A right trapezoid has no axis of symmetry and no rotational symmetry of higher order (only order <InlineMath math="1" />, which is the initial position).

*   Lines of symmetry: <InlineMath math="0" />
*   Rotational symmetry: <InlineMath math="1" />

This figure satisfies the condition (since <InlineMath math="0 \le 2" /> and <InlineMath math="1 \le 2" />).

#### Analyzing Regular Pentagon

A regular pentagon has <InlineMath math="5" /> equal sides.

*   Lines of symmetry: <InlineMath math="5" />
*   Rotational symmetry: <InlineMath math="5" />

This figure does **not** satisfy the condition.

#### Analyzing Equilateral Triangle

An equilateral triangle has <InlineMath math="3" /> equal sides.

*   Lines of symmetry: <InlineMath math="3" />
*   Rotational symmetry: <InlineMath math="3" />

This figure does **not** satisfy the condition.

#### Analyzing Kite (Not a Square)

A kite has one main axis of symmetry.

*   Lines of symmetry: <InlineMath math="1" />
*   Rotational symmetry: <InlineMath math="1" />

This figure satisfies the condition.

#### Conclusion

The plane figures that satisfy the condition are:
1. Right trapezoid.
2. Kite (not a square).

Thus, there are <InlineMath math="2" /> plane figures that satisfy the condition.


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