Circle and Triangle Area Problems

The video tutorial covers various problems related to areas in circles, including finding the area of shaded regions, equilateral triangles with inscribed circles, and calculating areas in square handkerchiefs with circular designs. Each problem is explained step-by-step, with formulas and calculations demonstrated to find the required areas.

What is the relationship between the diameters AB and CD in the circle problem?

• They are tangent.

• They are parallel.

• They are perpendicular.

• They are equal.

How is the radius of the smaller circle determined?

• By dividing the diameter by 3.

• By multiplying the diameter by 2.

• By dividing the diameter by 2.

• By adding the diameter to the radius of the larger circle.

Which formula is used to find the area of the shaded region?

• Area of semicircle plus area of triangle.

• Area of smaller circle plus area of semicircle minus area of triangle.

• Area of triangle plus area of smaller circle.

• Area of smaller circle minus area of semicircle.

What is the area of the smaller circle if its radius is 3.5 cm?

• 11 cm²

• 66.5 cm²

• 77 cm²

• 38.5 cm²

In the equilateral triangle problem, what is the radius of the circles drawn at each vertex?

• One-third the length of the side of the triangle.

• Twice the length of the side of the triangle.

• Half the length of the side of the triangle.

• Equal to the side of the triangle.

How is the side length of the equilateral triangle determined?

• By dividing the area by the number of sides.

• By using the perimeter of the triangle.

• By measuring the height of the triangle.

• By using the area formula for an equilateral triangle.

What is the formula used to find the remaining area of the handkerchief?

• Area of square minus area of one circle.

• Area of square minus 9 times area of a circle.

• Area of square plus area of a circle.

• Area of square minus area of a triangle.

How is the side length of the square handkerchief determined?

• By multiplying the radius by 3.

• By subtracting the radius from the diameter.

• By adding the diameters of three circles.

• By adding the radii of the circles.

What is the area of the quadrant in the circle problem?

• 77/8 cm²

• 1620.5 cm²

• 66.5 cm²

• 49/8 cm²

How is the area of the shaded region in the quadrant problem calculated?

• By adding the area of the triangle to the quadrant.

• By subtracting the area of the triangle from the quadrant.

• By dividing the area of the triangle by the quadrant.

• By multiplying the area of the triangle by the quadrant.