Tembereng Lingkaran - Matematika Kelas XI Kurikulum Merdeka

Summary

In this video, the topic of circle segments is discussed as part of the 11th-grade mathematics curriculum. The host explains the concept of a segment, which is the area within a circle bounded by a chord and an arc. The video covers how to calculate the area of a circle segment by subtracting the area of a triangle from the area of a sector. Using a specific example with a 21 cm radius and a 90-degree central angle, the video walks viewers through the process of calculating the segment's area. The session concludes with a practice problem for viewers to solve.

Takeaways

• 😀 Tebereng is a region inside a circle bounded by a chord and an arc.
• 😀 The chord connects two points on the circle, while the arc is the curved segment between those two points.
• 😀 To find the area of a tebereng, you first need to calculate the area of the sector (juring) and subtract the area of the triangle formed by the chord.
• 😀 The formula to calculate the area of a sector is (central angle / 360) × π × r².
• 😀 The area of a triangle formed by two radii of the circle can be found using the formula (1/2) × base × height, where the base and height are both equal to the radius of the circle.
• 😀 The example problem demonstrated how to calculate the area of a tebereng using a circle with a radius of 21 cm and a central angle of 90°.
• 😀 The area of the sector (juring) in the example was calculated to be 346.5 cm² using the formula for the area of a sector.
• 😀 The area of the triangle formed by the two radii of the circle was 220.5 cm², as it is a right triangle.
• 😀 To find the area of the tebereng, subtract the area of the triangle from the area of the sector, resulting in an area of 126 cm² for the tebereng.
• 😀 In addition to solving the example problem, the video encourages viewers to practice similar problems to reinforce their understanding of calculating tebereng areas.

Q & A

What is a tebereng in the context of a circle?

A tebereng is a region inside a circle that is bounded by a chord (tali busur) and the arc (busur lingkaran) of the circle. It is a part of the circle enclosed by these two elements.

How is a tebereng different from a sector in a circle?

A tebereng is formed by a chord and the arc of the circle, whereas a sector is the area enclosed by two radii and the arc of the circle. A tebereng includes part of the area outside the central triangle of the sector.

What are the main components of a circle used to calculate the area of a tebereng?

The main components are the radius (jari-jari), the central angle (sudut pusat), the chord (tali busur), and the arc (busur lingkaran). These elements help in calculating the area of the tebereng.

How is the area of a tebereng calculated?

The area of a tebereng is calculated by subtracting the area of the triangle formed by the two radii and the chord from the area of the sector. The formula is: Area of tebereng = Area of sector - Area of triangle.

What formula is used to find the area of a sector in a circle?

The formula for the area of a sector is: Area of sector = (θ / 360) * π * r², where θ is the central angle in degrees, and r is the radius of the circle.

In the example provided, what are the given values used to calculate the tebereng?

The given values are a radius (r) of 21 cm and a central angle (θ) of 90°.

How do you calculate the area of the triangle inside the sector?

To calculate the area of the triangle, use the formula for the area of a right triangle: (1/2) * base * height. In this case, both the base and height are the radius of the circle, so the area of the triangle is (1/2) * 21 * 21 = 220.5 cm².

What is the area of the sector in the example, and how is it calculated?

The area of the sector is 346.5 cm². This is calculated using the formula for the area of a sector, substituting θ = 90° and r = 21 cm. The result is: (90/360) * (22/7) * 21 * 21 = 346.5 cm².

What is the final area of the tebereng in the example, and how is it found?

The final area of the tebereng is 126 cm². It is found by subtracting the area of the triangle (220.5 cm²) from the area of the sector (346.5 cm²): 346.5 cm² - 220.5 cm² = 126 cm².

What should be done to ensure students understand how to calculate the area of a tebereng?

Students should practice using the formula for the sector and triangle areas. It is important to first understand the geometry of the circle, identify the components like the chord and sector, and then apply the correct formulas step by step.