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

Learning Objectives Identify the basic geometric shapes (triangles, semicircles, quarter circles) within a compound figure. Recall and apply the area formulas for triangles, semicircles, and quarter circles. Decompose complex compound figures into simpler, familiar shapes. Calculate the area of each component shape accurately. Combine (add or subtract) the areas of component shapes to find the total area of a compound figure. 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? 🤔 It's all about breaking down complex shapes! In this lesson, you'll learn how to find the area of figures made up of triangles, semicircles, and qu...

TermDefinitionExample Compound FigureA geometric shape that is formed by combining two or more basic geometric shapes, such as triangles, rectangles, circles, or parts of circles.A house shape made by putting a triangle (roof) on top of a rectangle (walls). AreaThe amount of two-dimensional space a shape or surface covers, measured in square units (e.g., square inches, square meters).The area of a square with sides of 5 cm is 25 square centimeters (25 cm²). TriangleA polygon with three straight sides and three angles. Its area depends on its base and height.A right triangle with a base of 4 units and a height of 3 units. SemicircleExactly half of a circle. Its area is half the area of a full circle with the same radius.The shape of a rainbow or half of a pizza. Quarter CircleExactly one-f...

Area of a Triangle $$A = \frac{1}{2}bh$$ Use this formula to find the area of any triangle, where 'b' is the length of the base and 'h' is the perpendicular height from the base to the opposite vertex. Area of a Semicircle $$A = \frac{1}{2}\pi r^2$$ Use this formula to find the area of a semicircle, where 'r' is the radius of the full circle from which the semicircle is formed. Remember to use $\pi \approx 3.14$ for calculations. Area of a Quarter Circle $$A = \frac{1}{4}\pi r^2$$ Use this formula to find the area of a quarter circle, where 'r' is the radius of the full circle from which the quarter circle is formed. Remember to use $\pi \approx 3.14$ for calculations.