Calculating Areas of Shaded Regions in Composite Figures

This lesson explores calculating the area of shaded regions in composite figures. It covers methods for finding the area of larger shapes and subtracting the area of smaller, non-shaded shapes. Examples include using rectangles, parallelograms, trapezoids, and triangles to determine the shaded area. The lesson emphasizes breaking down complex shapes into simpler components for easier calculation.

How do you calculate the area of a rectangle?

• Sum of all sides

• Base times height

• Length plus width

• One-half base times height

What formula is used to find the area of a parallelogram?

• Length plus width

• Base times height

• Base plus height

• One-half base times height

What is the first step in finding the area of a shaded region within composite figures?

• Find the area of the larger shape only

• Multiply the areas of the shaded and unshaded shapes

• Add the areas of all shapes together

• Subtract the area of the unshaded shape from the shaded shape

How is the area of the shaded region within a rectangle and parallelogram composite figure calculated?

• Adding the areas of both shapes

• Subtracting the parallelogram's area from the rectangle's

• Multiplying the areas of both shapes

• Dividing the rectangle's area by the parallelogram's

In the context of composite figures, why is it sometimes necessary to subtract the area of one shape from another?

• To accurately determine the area of the shaded region

• Because addition of areas is mathematically incorrect

• To find the area of the unshaded region

• To simplify the calculation process

Which formula is applied to find the area of a trapezoid?

• One-half base times height

• Base times height

• Length plus width

• One-half of the sum of the two bases times height

What is the area of the shaded region when subtracting a triangle from a trapezoid?

• 195 feet squared

• 255 feet squared

• 60 feet squared

• 135 feet squared

How do you find the base of a triangle when it's not directly given?

• Add the lengths of adjacent sides

• Subtract adjacent side lengths from the total length

• Multiply the heights of adjacent shapes

• Divide the area by the height

What is the final step in calculating the shaded area in a composite figure involving subtraction?

• Add the areas of the shaded and unshaded shapes

• Divide the total area by the unshaded area

• Subtract the unshaded shape's area from the total

• Multiply the areas of the shaded and unshaded shapes

What is the area of the shaded region in the complex figure involving a rectangle and an adjacent triangle?

• 252 inches squared

• 12 inches squared

• 240 inches squared

• 226 inches squared