Triangles and Pentagons Area Calculations

The video tutorial explains how to find the area of a regular pentagon inscribed in a circle. It begins by dividing the pentagon into congruent triangles and calculating the central angle. Using trigonometry, the side lengths of the triangles are determined. The area of one triangle is calculated and then multiplied by five to find the total area of the pentagon. The tutorial provides a step-by-step approach, using trigonometric functions like sine and cosine, to solve the problem.

What is the radius of the circle in which the pentagon is inscribed?

• 5 units

• 6 units

• 8 units

• 10 units

How many congruent triangles can the pentagon be divided into?

• 6

• 5

• 4

• 3

What is the measure of the central angle of each triangle?

• 60 degrees

• 72 degrees

• 90 degrees

• 108 degrees

What is the apothem in the context of this problem?

• The radius of the circle

• The height of the triangle

• The base of the triangle

• The hypotenuse of the triangle

What angle does the apothem split the central angle into?

• 18 and 18 degrees

• 45 and 45 degrees

• 24 and 24 degrees

• 36 and 36 degrees

Which trigonometric function is used to find the side length opposite the 36-degree angle?

• Tangent

• Sine

• Secant

• Cosine

What is the approximate length of the side opposite the 36-degree angle?

• 6.5

• 3.5

• 4.7

• 5.8

Which trigonometric function is used to find the apothem?

• Tangent

• Cosine

• Sine

• Cosecant

What is the approximate length of the apothem?

• 4.7

• 6.5

• 5.5

• 7.2

What is the base of the triangle when calculating its area?

• 12.8

• 9.4

• 6.5

• 4.7