Area between two shapes

Learning Objectives Calculate the area of a composite shape by subtracting the area of an inner shape from an outer shape. Identify the larger and smaller shapes in a diagram to correctly set up an area subtraction problem. Apply area formulas for common polygons (squares, rectangles, triangles) and circles in multi-step problems. Solve problems involving the area of an annulus (the region between two concentric circles). Use given dimensions to find missing lengths required for area calculations. Set up and solve word problems involving the area of shaded regions. Interpret geometric diagrams to determine the necessary steps for finding the area between shapes. Ever wondered how to calculate the area of a doughnut or the surface of a running track? 🍩 It's simpler th...

TermDefinitionExample Composite ShapeA geometric figure made from two or more basic shapes. In this context, it often involves one shape being removed from another.A square with a circular hole in the center. Shaded RegionThe specific area within a diagram that needs to be calculated. It typically represents the difference between the areas of two shapes.In a diagram of a circle inside a square, the area in the corners of the square, outside the circle, might be the shaded region. Area of the Outer Shape (A_large)The total area of the larger, enclosing shape.For a picture frame, this is the area of the entire frame including the picture space. Area of the Inner Shape (A_small)The area of the shape that is being 'removed' or is not part of the region of interest.For a picture fra...

The Subtraction Principle A_{region} = A_{large} - A_{small} This is the fundamental rule for finding the area between two shapes. Calculate the area of the entire outer shape, then calculate the area of the inner shape (the 'hole'), and subtract the latter from the former. Area of an Annulus A = \pi R^2 - \pi r^2 = \pi(R^2 - r^2) A specific application of the Subtraction Principle for the area between two concentric circles. 'R' is the radius of the outer circle and 'r' is the radius of the inner circle. Essential Area Formulas (Review) Rectangle: A = l \times w | Triangle: A = \frac{1}{2}bh | Circle: A = \pi r^2 These are the foundational formulas you must know to calculate the areas of the component shapes before you can apply the Sub...