MATEMATIKA WAJIB KELAS XI MATERI LINGKARAN DARI BUKU PKS : SEGI-N BERATURAN

Summary

This video provides a detailed lesson on regular polygons inscribed in circles, specifically focusing on calculating their perimeter and area. The presenter explains the properties of regular polygons, such as equal side lengths, and how to use trigonometric rules like the cosine and sine laws to determine the perimeter and area when the radius or side length is known. Through step-by-step examples, including a regular octagon and dodecagon, the viewer learns to apply these formulas for calculating side lengths and areas, offering valuable insight into geometric problem-solving.

Takeaways

• 😀 A regular polygon (n-gon) is a flat shape with 'n' sides, all of which have the same length.
• 😀 The perimeter of a regular polygon can be found by multiplying the number of sides (n) by the length of one side (s).
• 😀 A regular polygon can be divided into 'n' congruent isosceles triangles, each with two sides equal to the radius of the circumscribed circle.
• 😀 The interior angle between two adjacent sides in a regular polygon is calculated as 360° divided by the number of sides (n).
• 😀 The area of a regular polygon can be computed by multiplying the number of sides (n) by the area of one of its isosceles triangles.
• 😀 The law of cosines can be used to find missing side lengths in triangles within a regular polygon, such as the side length (s) when the radius (r) is known.
• 😀 The area of a triangle within a regular polygon can be calculated using the formula (1/2) * base * height or (1/2) * r^2 * sin(θ), where θ is the angle between the two equal sides.
• 😀 If the side length is unknown but the radius (r) of the circumscribed circle is given, the side length can be determined using the law of cosines.
• 😀 For polygons inscribed in circles, if only the radius is provided, formulas can still be used to find the perimeter and area by deriving side length from the radius.
• 😀 Examples from the script illustrate calculating both the perimeter and area for polygons with various numbers of sides (such as octagons and dodecagons), using known formulas and trigonometric rules.

Q & A

What is a regular polygon, and how is it characterized?

A regular polygon is a flat geometric shape with all sides of equal length and all interior angles of equal measure. Its most defining characteristic is that all its sides are congruent.

How do you calculate the perimeter of a regular polygon?

The perimeter of a regular polygon can be calculated by multiplying the number of sides (n) by the length of one side (s). The formula is: Perimeter = n * s.

How can you calculate the area of a regular polygon?

The area of a regular polygon can be calculated using the formula: Area = n * (Area of one triangle), where the area of one triangle can be calculated using the formula 1/2 * r^2 * Sin(360/n), where r is the radius of the circumscribed circle.

What is the formula for finding the side length of a regular polygon when the radius of the circumscribed circle is known?

To find the side length (s) of a regular polygon when the radius (r) is known, you can use the formula: s = r * √(2 - 2 * cos(360/n)), where n is the number of sides.

How do you calculate the angle formed by the vertices of a regular polygon?

The angle formed by the vertices of a regular polygon, often referred to as the central angle, can be calculated using the formula: Central angle = 360° / n, where n is the number of sides.

What trigonometric law is used to calculate the side length of a regular polygon when the radius is known?

The Law of Cosines is used to calculate the side length of a regular polygon when the radius is known. It relates the side length to the radius and the central angle between adjacent sides.

In the example of an octagon with a radius of 4 cm, how do you find the side length?

To find the side length of an octagon with a radius of 4 cm, you use the Law of Cosines. First, calculate the central angle (360° / 8 = 45°), then apply the formula for the side length: s = r * √(2 - 2 * cos(45°)).

What is the formula for the area of a regular polygon using the radius and the number of sides?

The area of a regular polygon can be calculated using the formula: Area = n/2 * r^2 * Sin(360/n), where n is the number of sides, and r is the radius of the circumscribed circle.

What is the central angle of a regular polygon with 12 sides?

The central angle of a regular polygon with 12 sides is 360° / 12 = 30°.

How do you calculate the perimeter of a regular dodecagon with a radius of 8 cm?

To calculate the perimeter of a regular dodecagon with a radius of 8 cm, first calculate the side length using the Law of Cosines. Then, multiply the side length by the number of sides (12). The formula for the perimeter is: Perimeter = 12 * s.