Equilateral Triangle and Circle Areas

The video tutorial explains how to find the area of a blue shaded region formed by three circle sectors inscribed in an equilateral triangle. The process involves calculating the area of the triangle using a specific formula and the area of the circle sectors using another formula. The difference between these areas gives the area of the shaded region. The tutorial provides a step-by-step approach, including determining the angle of the sectors and performing the necessary calculations to arrive at the exact and decimal values of the shaded area.

What is the radius of the circles inscribed in the triangle?

• 2

• 3

• 4

• 5

What is the length of each side of the equilateral triangle?

• 6

• 7

• 8

• 9

Which formula is used to calculate the area of an equilateral triangle?

• s^2

• 1/2 * base * height

• sqrt(3)/4 * s^2

• pi * r^2

What is the formula for the area of a sector of a circle?

• pi * r^2

• theta/360 * pi * r^2

• 1/2 * base * height

• s^2

How many sectors are there in the problem?

• 4

• 3

• 2

• 1

What is the measure of each angle in the equilateral triangle?

• 90 degrees

• 60 degrees

• 45 degrees

• 30 degrees

What is the value of theta used in the sector area calculation?

• 90

• 60

• 45

• 30

What is the exact expression for the area of the shaded region?

• 8 sqrt(3) - 16 pi

• 16 sqrt(3) - 8 pi

• 16 pi - 8 sqrt(3)

• 8 pi - 16 sqrt(3)

What is the decimal value of the area of the shaded region?

• 2.58

• 5.00

• 3.14

• 4.20

What is the final step in calculating the area of the shaded region?

• Adding the areas of the sectors

• Calculating the triangle's perimeter

• Finding the radius

• Subtracting the area of the sectors from the triangle