Finding the Area of Shaded Regions in Polygons

This instructional video explains how to find the area of shaded regions, a popular problem type. It covers calculating the area of a large circle and subtracting the area of a smaller circle to find the shaded area. The video also demonstrates finding the area of a square and subtracting the area of a circle within it. The instructor provides step-by-step guidance, including using the formula for the area of a circle (PI R squared) and converting pi to a real number for practical calculations. The video concludes with tips for solving these types of problems.

What is the formula used to calculate the area of a circle?

• Area = 2 * radius squared

• Area = pi * diameter

• Area = pi * radius squared

• Area = 2 * pi * radius

What is the area of a circle with a radius of 10 units?

• 100 pi units squared

• 20 pi units squared

• 10 pi units squared

• 200 pi units squared

How do you find the area of the shaded region between two concentric circles?

• Multiply the areas of both circles

• Subtract the area of the smaller circle from the larger circle

• Add the areas of both circles

• Divide the area of the larger circle by the smaller circle

What is the area of the smaller inner circle if its radius is 7 units?

• 28 pi units squared

• 49 pi units squared

• 14 pi units squared

• 7 pi units squared

What is the area of a square with side length 18 units?

• 324 units squared

• 36 units squared

• 180 units squared

• 18 units squared

How is the diameter of a circle related to its radius?

• Diameter is twice the radius

• Diameter is half the radius

• Diameter is equal to the radius

• Diameter is three times the radius

What is the area of a circle with a radius of 9 units?

• 81 pi units squared

• 18 pi units squared

• 9 pi units squared

• 27 pi units squared

How do you calculate the area of a shaded region within a square after subtracting a circle?

• Add the area of the circle to the area of the square

• Multiply the area of the circle by the area of the square

• Divide the area of the square by the area of the circle

• Subtract the area of the circle from the area of the square

What is the approximate real number value of pi used in the calculations?

• 3.14159

• 22/7

• 3.14

• 3.142

What is the final area of the shaded region in the square and circle problem?

• 254.34 units squared

• 69.66 units squared

• 81 pi units squared

• 324 units squared