lesson
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Basketball courts, running tracks, and skate park ramps all combine straight borders with smooth, circular curves.
A composite figure is any shape made by putting together two or more basic geometric shapes.
How do we measure the flat surface inside these mixed shapes?
Slicing Up Circles
A full circle has an area of A=Οr2, where the radius (r) is the distance from the center point to the outer edge.
A semicircle is exactly half of a circle, while a quarter circle is one fourth of a circle.
πCreate an interactive visual breakdown comparing a full circle, a semicircle, and a quarter circle side by side. Each shape is displayed inside a sleek card on a light background (#f8f9fa). Shape 1: Full circle (diameter line in dotted gray, radius r labeled in blue #2563eb, formula A = ΟrΒ²). Shape 2: Semicircle (flat base labeled diameter d, radius r going up, formula A = Β½ΟrΒ²). Shape 3: Quarter circle (two perpendicular straight edges labeled r, 90Β° corner symbol, formula A = ΒΌΟrΒ²). Underneath, show a toggle or slider for radius r = 4 cm showing calculated areas using Ο β 3.14.
What happens when a curved shape attaches directly onto a flat-sided polygon?
Adding Regions Together
When shapes sit side-by-side without overlapping, you find the area of each separate region and add them together.
Let's find the area of a basketball key made of a 12Β ft by 19Β ft rectangle attached to a semicircle.
πCreate a diagram of a basketball free-throw key. The main body is a vertical rectangle (width 12 ft, height 19 ft) colored light blue (#dbeafe). On top of the rectangle sits a semicircle colored light amber (#fef3c7) whose straight base matches the 12 ft top edge. Show dotted lines indicating the split between the two shapes. Label: Rectangle Area = 12 Γ 19 = 228 sq ft. Label: Semicircle Diameter = 12 ft β Radius r = 6 ft. Semicircle Area = Β½ Γ 3.14 Γ 6Β² = 56.52 sq ft. Total Area badge at bottom: 228 + 56.52 = 284.52 sq ft.
The rectangle's top side of 12Β ft serves as the semicircle's diameter, which means the radius is half of that: r=6Β ft.