Area and Radius of Circles

This video tutorial explains how to calculate the area of composite figures, focusing on those containing semicircles. It provides step-by-step examples, including figures with rectangles, semicircles, squares, and quarter circles. The tutorial also covers the use of basic geometric formulas and offers tips for exact and approximate calculations. By the end, viewers will understand how to approach and solve area problems involving various composite shapes.

What is the formula for the area of a semicircle?

• 2πr²

• ¼πr²

• ½πr²

• πr²

In the first example, what is the area of the rectangle?

• 50 square ft

• 60 square ft

• 70 square ft

• 80 square ft

How is the radius of the semicircle determined in the first example?

• It is equal to the length of the rectangle.

• It is equal to the width of the rectangle.

• It is half the width of the rectangle.

• It is half the length of the rectangle.

In the second example, what is the diameter of the semicircle?

• 20 cm

• 5 cm

• 10 cm

• 15 cm

What is the total area of the composite figure in the second example?

• 80 + 12.5π square cm

• 100 + 12.5π square cm

• 110 + 12.5π square cm

• 90 + 12.5π square cm

In the third example, what is the formula used to find the area of the quarter circle?

• ½πr²

• ¼πr²

• πr²

• 2πr²

What is the radius of the quarter circle in the third example?

• 6 in

• 8 in

• 9 in

• 7 in

In the fourth example, what is the radius of the semicircle?

• 9 units

• 8 units

• 7 units

• 6 units

How is the area of the triangles calculated in the fourth example?

• Base times height

• ½ base times height

• Base plus height

• Base minus height

What is the total area of the composite figure in the fourth example?

• 62 + 32π square units

• 82 + 32π square units

• 72 + 32π square units

• 52 + 32π square units