Area of compound figures with triangles, semicircles, and quarter circles

Learning Objectives Identify basic geometric shapes (triangles, semicircles, quarter circles, rectangles) within a complex compound figure. Recall and apply the area formulas for triangles, circles, semicircles, and quarter circles. Decompose compound figures into simpler, familiar geometric shapes. Calculate the area of individual triangles, semicircles, and quarter circles given their dimensions. Calculate the total area of compound figures by summing or subtracting the areas of their component shapes. Use the approximation of π (pi ≈ 3.14) in area calculations involving circles. Solve real-world problems involving the area of compound figures. Ever wondered how much paint you'd need for a uniquely shaped wall, or how much grass seed for a garden with curved edges?...

TermDefinitionExample Compound FigureA geometric shape that is made up of two or more simpler basic shapes, such as rectangles, triangles, circles, semicircles, or quarter circles.A shape that looks like a house, made by combining a rectangle (the main house) and a triangle (the roof). DecompositionThe process of breaking down a complex compound figure into its simpler, recognizable geometric components to make calculations easier.To find the area of an 'L' shaped room, you can decompose it into two rectangles and find the area of each. AreaThe amount of two-dimensional space a shape covers, measured in square units (e.g., square inches, square meters).If a square tile is 1 foot by 1 foot, its area is 1 square foot. Radius (r)The distance from the center of a circle to any point...

Area of a Triangle $$A = \frac{1}{2} \times b \times h$$ To find the area of a triangle, multiply half of its base (b) by its height (h). The base and height must be perpendicular to each other. Area of a Circle $$A = \pi \times r^2$$ To find the area of a full circle, multiply pi (\pi \approx 3.14) by the square of its radius (r). Remember, $r^2$ means $r \times r$. Area of a Semicircle $$A = \frac{1}{2} \times \pi \times r^2$$ To find the area of a semicircle, calculate the area of a full circle with the same radius and then divide by 2. Use \pi \approx 3.14. Area of a Quarter Circle $$A = \frac{1}{4} \times \pi \times r^2$$ To find the area of a quarter circle, calculate the area of a full circle with the same radius and then divide by 4. Use \pi \approx 3...