Area between two shapes

Learning Objectives Identify the outer and inner shapes in a given problem. Recall and apply area formulas for basic 2D shapes (rectangles, squares, circles). Calculate the area of a larger, outer shape. Calculate the area of a smaller, inner shape contained within the outer shape. Subtract the area of the inner shape from the outer shape to find the area between them. Solve real-world problems involving the area between two shapes. Express the final area with appropriate square units. Imagine you're painting a wall with a window in it. How would you figure out just the area you need to paint, not including the window? 🤔 In this lesson, you'll learn how to calculate the space between two shapes, like the area of a frame around a picture or the grass around a po...

TermDefinitionExample AreaThe amount of surface a two-dimensional shape covers, measured in square units.A square with sides of 4 cm has an area of 16 square centimeters ($16 ext{ cm}^2$). Outer ShapeThe larger shape that completely encloses another shape.In a problem about a rectangular garden with a circular pond, the rectangular garden is the outer shape. Inner ShapeThe smaller shape that is completely contained within a larger shape.In a problem about a rectangular garden with a circular pond, the circular pond is the inner shape. Area Between ShapesThe region that is part of the outer shape but not part of the inner shape; found by subtracting the inner area from the outer area.The grassy area in a rectangular garden surrounding a circular pond is the 'area between shapes'...

Area of a Rectangle $A = l \times w$ To find the area of a rectangle, multiply its length ($l$) by its width ($w$). This is used for rectangular outer or inner shapes. Area of a Square $A = s^2$ To find the area of a square, multiply its side length ($s$) by itself. This is a special case of a rectangle where length equals width. Area of a Circle $A = \pi r^2$ To find the area of a circle, multiply pi ($\pi \approx 3.14$) by the square of its radius ($r$). This is used for circular outer or inner shapes. Area Between Two Shapes $A_{\text{between}} = A_{\text{outer}} - A_{\text{inner}}$ To find the area of the region that is part of a larger (outer) shape but not part of a smaller (inner) shape contained within it, subtract the area of the inner shape from the...