Composite Figures and Area Formulas

The video tutorial covers how to solve problems involving composite figures, specifically those with parts of circles. It explains how to break down these figures into simpler shapes, such as semi-circles and triangles, to calculate their areas. The tutorial provides step-by-step instructions for calculating the area of a semi-circle and a triangle, emphasizing the importance of dividing by two for semi-circles. It also includes an example problem involving a rectangle and a semi-circle, demonstrating the process of finding the total area of composite figures.

What is the first step in solving problems involving composite figures?

• Find the volume of the figure.

• Break the figure into simpler shapes.

• Draw the figure to scale.

• Calculate the perimeter of the figure.

Why is it suggested to break composite figures into the fewest number of shapes?

• To avoid using a calculator.

• To increase the number of calculations.

• To make the figure look more complex.

• To use fewer formulas.

In the given composite figure, what shapes are identified?

• Two semi-circles

• A semi-circle and a triangle

• Two rectangles

• A rectangle and a circle

What is the formula for the area of a semi-circle?

• pi times diameter divided by two

• pi times radius squared divided by two

• pi times diameter

• pi times radius squared

Why is it important to divide by two when calculating the area of a semi-circle?

• To convert the area into square units.

• Because a semi-circle is half of a circle.

• To find the perimeter instead of the area.

• To simplify the calculation.

What is the formula for the area of a triangle?

• Base minus height

• Base times height

• One-half base times height

• Base plus height

How do you determine the base of the triangle in the composite figure?

• By using the radius of the semi-circle.

• By adding the lengths of the two sides of the triangle.

• By dividing the diameter of the circle by two.

• By measuring the height of the triangle.

What is the total area of the composite figure consisting of a semi-circle and a triangle?

• 100 square feet

• 59.25 square feet

• 20 square feet

• 39.25 square feet

What shapes make up the new composite figure?

• Two rectangles

• A square and a circle

• A rectangle and a semi-circle

• Two triangles

What is the formula for the area of a rectangle?

• Length plus width

• Base times height

• Length times width

• Base plus height