Composite Area and Shape Analysis

Mrs. Zapia's lesson covers composite area problems in the coordinate plane. Students learn to decompose regions into familiar shapes like triangles, quadrilaterals, and circles to find areas. Three examples are provided: calculating the area of a shaded region with circles, a rectangle with a semicircle, and a shaded region in a square. The lesson emphasizes using known formulas and subtraction to find composite areas.

What is the main focus of the lesson on composite area problems?

• Calculating the volume of 3D shapes

• Identifying the types of polygons

• Finding the perimeter of composite figures

• Determining the area of regions with polygonal boundaries

In Example 1, what is the first step in finding the composite area of the shaded region?

• Calculate the circumference of the larger circle

• Find the area of the larger circle

• Subtract the area of the smaller circle from the larger circle

• Determine the diameter of the smaller circle

How do you find the area of the smaller circle in Example 1?

• Multiply the diameter by π

• Use the formula πr² with the radius of the smaller circle

• Subtract the radius from the larger circle's radius

• Divide the area of the larger circle by 2

In Example 2, what is the relationship between the width of the rectangle and the diameter of the semicircle?

• The width is twice the diameter

• The width is half the diameter

• The width is equal to the diameter

• The width is unrelated to the diameter

What is the formula used to find the area of the semicircle in Example 2?

• πr²

• ½ × πr²

• 2πr

• πd

In Example 3, why can't the formula for a triangle be directly used to find the area of the shaded region?

• The triangle is not in the coordinate plane

• The triangle is not a right triangle

• The base and height are not labeled

• The triangle is too large

What is the strategy used in Example 3 to find the area of the shaded region?

• Add the areas of all triangles

• Divide the area of the square by the number of triangles

• Subtract the areas of the triangles from the square

• Multiply the areas of the triangles

What is the total area of the square in Example 3 before subtracting the triangles?

• 200 cm²

• 300 cm²

• 400 cm²

• 500 cm²

In the lesson summary, what is emphasized as the key method for finding the area of composite figures?

• Guessing the area based on size

• Breaking down figures into familiar shapes

• Using only the formula for circles

• Measuring directly with a ruler

What is the final step in finding the area of a composite figure with multiple shapes?

• Divide the total area by the number of shapes

• Multiply all areas together

• Subtract the smallest area from the largest

• Add or subtract the areas as needed