Geometry: Area and Length Problems

The video tutorial explains how to find the area of a shaded portion in a geometric diagram. It involves understanding the given rectangle and circle, calculating the area of a segment using Pythagoras theorem, and finally determining the shaded area by subtracting the segment area from the rectangle area. The tutorial provides a step-by-step approach to solving the problem, including the use of geometric properties and calculations.

What is the main objective of the problem discussed in the video?

• To determine the volume of a cylinder

• To calculate the area of a shaded portion

• To measure the length of a diagonal

• To find the perimeter of a rectangle

What is the length of side AB of the rectangle?

• 3

• 2

• √3

• 2√3

What is the role of point O in the diagram?

• It is a vertex of the rectangle

• It is the center of the circle

• It is the midpoint of AB

• It is the endpoint of a diagonal

What is the length of side AD of the rectangle?

• 2√3

• 1

• 2

• √3

What is the length of the segment AB?

• 2√3

• 1

• 2

• √3

What is the length of the segment BC?

• 2√3

• √3

• 2

• 1

What is the length of the segment CD?

• 1

• 2

• 2√3

• √3

How is the area of the shaded portion determined?

• By multiplying the areas of the rectangle and the segment

• By dividing the area of the rectangle by the segment

• By subtracting the area of the segment from the rectangle

• By adding the area of the rectangle and the segment

What theorem is used to calculate the segment area?

• Fermat's theorem

• Pythagoras theorem

• Thales theorem

• Euclid's theorem

What is the relationship between OE and the rectangle?

• OE is the radius of the circle

• OE is perpendicular to BC

• OE is parallel to AB

• OE is the diagonal of the rectangle