Area and Geometry Problems

The video tutorial covers various geometry problems involving area calculations of composite shapes. It begins with calculating the area of a banner made of a square and semicircle, followed by determining the carpet area and cost for a closet. The tutorial also includes sketching and calculating the area of a hexagon, a bookmark with semicircles, and a Palladium window with a shade. Each problem is broken down into steps, demonstrating the use of formulas for squares, rectangles, circles, and triangles.

What is the total area of a banner made of a square and a semicircle if the side of the square is 26 inches?

• 941.33 square inches

• 900.00 square inches

• 850.50 square inches

• 1000.00 square inches

How much carpet is needed to cover a closet floor composed of two shapes, if the total area is 61 square feet?

• 40 square feet

• 61 square feet

• 50 square feet

• 70 square feet

If the cost of carpeting is $2.50 per square foot, what is the total cost to carpet a 61 square foot area?

• $152.50

• $100.00

• $200.00

• $250.00

How many sides does a hexagon have?

• Eight

• Seven

• Six

• Five

What is the area of a hexagon if it is divided into a trapezoid and a rectangle, with areas 9 and 21 respectively?

• 20 square units

• 35 square units

• 25 square units

• 30 square units

What is the area of a bookmark shaped like a rectangle with semicircles at both ends, if the rectangle is 12 cm long and 4 cm wide?

• 80.00 square cm

• 70.00 square cm

• 50.00 square cm

• 60.56 square cm

If a Palladium window is composed of a semicircular top and a square bottom, what is the total area if the square's side is 10 inches?

• 2228 square inches

• 2000 square inches

• 2500 square inches

• 1800 square inches

What is the radius of the semicircle in the Palladium window if the diameter is 20 inches?

• 10 inches

• 15 inches

• 20 inches

• 25 inches

How much area does the shade add to the Palladium window if it extends 4 inches beyond the perimeter?

• 2500 square inches

• 3500 square inches

• 3016 square inches

• 4000 square inches

What is the area of a square if its side length is 5 feet?

• 35 square feet

• 30 square feet

• 25 square feet

• 20 square feet