Proportional Relationships and Area Calculations

The video tutorial covers various geometry problems, including calculating the area of a circle, finding the area of a shaded region by subtracting circles from a rectangle, and determining the area of a clock face using its circumference. It also explores proportional relationships and constants of proportionality, using examples like reading rates. The tutorial emphasizes different methods for solving area problems and verifying results.

What is the area of a circle with a diameter of 12 inches when folded into a quarter circle?

• 113.04 square inches

• 14.13 square inches

• 28.26 square inches

• 56.52 square inches

How do you find the area of a shaded region within a rectangle?

• Subtract the areas of circles from the rectangle

• Add the areas of all shapes

• Divide the area of the rectangle by the number of circles

• Multiply the areas of all shapes

Given a clock face with a circumference of 36 inches, how do you find its area?

• Divide the circumference by 2

• Find the radius from the circumference and use the area formula for a circle

• Multiply the circumference by the diameter

• Use the formula for the area of a square

Which of the following pairs of quantities are proportional?

• Area and radius

• Radius and diameter

• Diameter and area

• Circumference and area

What is the constant of proportionality between the radius and the diameter of a circle?

• 4

• 1/2

• 2

• π

How can you find the area of a composite shape by breaking it into simpler shapes?

• By adding the areas of the simpler shapes

• By subtracting the areas of the simpler shapes

• By dividing the area of the largest shape by the number of smaller shapes

• By multiplying the areas of the simpler shapes

If Elena reads 4 pages for every 5 pages Jada reads, what is the constant of proportionality?

• 4

• 1.25

• 0.8

• 5

What is the area of a triangle with a base of 2 meters and a height of 2 meters?

• 2 square meters

• 8 square meters

• 1 square meter

• 4 square meters

How do you calculate the area of a large rectangle with a triangular section cut out?

• Add the area of the triangle to the rectangle

• Subtract the area of the triangle from the rectangle

• Multiply the area of the triangle by the rectangle

• Divide the area of the rectangle by the triangle

What does a constant of proportionality of 1.25 between two reading rates imply?

• One person reads 1.25 times faster than the other

• Both read at the same speed

• One person reads 1.25 pages for every page the other reads

• One person reads 0.8 pages for every page the other reads