Calculating the Area of Polygons with the Law of Sines

The video tutorial explains how to calculate the area of various polygons by dividing them into triangles. It covers the use of trigonometric functions, specifically the sine function, to find the area of triangles when the height is unknown. The tutorial provides step-by-step examples for calculating the area of a square, nonagon, pentagon, and octagon by using isosceles triangles and the law of sines. The teacher emphasizes the importance of understanding the relationship between angles and sides in these calculations.

What is the formula to find the area of a triangle using one angle and the two adjacent sides?

• 0.5 * a * b * sin(C)

• a * b * sin(C)

• 0.5 * a * b * cos(C)

• a * b * cos(C)

If a triangle has sides of length 6 and an angle of 90 degrees between them, what is the area?

• 9

• 36

• 27

• 18

How many triangles are formed in a polygon when divided from the center if the total angle is 360 degrees and each angle is 90 degrees?

• 4

• 8

• 5

• 9

What is the degree measure of each angle in a nine-sided polygon divided into triangles from the center?

• 40 degrees

• 45 degrees

• 50 degrees

• 30 degrees

For a triangle with sides 11 and an angle of 40 degrees between them, what is the area of one triangle?

• 58.35

• 77.8

• 38.9

• 19.45

How many triangles are there in a polygon that is divided from the center with each angle measuring 72 degrees?

• 6

• 7

• 4

• 5

What is the total area of a polygon with five triangles, each having an area of 77.9?

• 389.5

• 311.6

• 155.8

• 194.75

What is the side length found using the law of sines if the opposite angle is 54 degrees and the known side is 15 with its opposite angle 72 degrees?

• 10.5

• 20.3

• 15

• 12.8

What is the area of a triangle with sides 15.7 and an angle of 45 degrees between them?

• 87.1

• 174.2

• 130.65

• 43.55

What is the total area of an eight-sided polygon if each triangle within it has an area of 87.1?

• 348.6

• 174.3

• 697.2

• 523.8