Area and perimeter mixed review

Learning Objectives Calculate the area and perimeter of complex composite figures by decomposing them into simpler shapes. Apply the Pythagorean theorem and trigonometric ratios (SOH CAH TOA) to determine unknown side lengths required for area and perimeter calculations. Determine the perimeter and area of polygons defined by vertices on a coordinate plane using the distance formula. Calculate the arc length and area of sectors of circles and incorporate them into composite figure problems. Calculate the area of regular polygons using the apothem and perimeter formula. Analyze word problems to distinguish between scenarios requiring area, perimeter, or both, and develop a multi-step solution strategy. Imagine you're designing a custom skate park or landscaping a backyar...

TermDefinitionExample Composite FigureA two-dimensional figure made up of two or more basic geometric shapes such as triangles, rectangles, and circles.An 'L-shaped' room can be seen as two rectangles combined. Its area is the sum of the areas of the two rectangles. Apothem (of a Regular Polygon)A line segment from the center of a regular polygon to the midpoint of a side, to which it is perpendicular.In a regular hexagon, the apothem is the height of one of the six equilateral triangles that form the hexagon, if you connect the vertices to the center. Sector of a CircleThe portion of a circle enclosed by two radii and the arc that connects them.A slice of pizza is a perfect example of a sector of a circle. Arc LengthThe distance along the curved line making up an arc, which is...

Area of a Regular Polygon A = \frac{1}{2}aP Used to find the area of a regular polygon. 'A' is the area, 'a' is the length of the apothem, and 'P' is the perimeter of the polygon. Arc Length and Sector Area Arc Length (L) = \frac{\theta}{360°} \times 2\pi r \quad | \quad \text{Sector Area (A)} = \frac{\theta}{360°} \times \pi r^2 Used to find the length of a part of a circle's circumference or the area of a 'slice' of a circle. 'θ' is the central angle in degrees and 'r' is the radius. Distance Formula d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} Used in coordinate geometry to find the distance between two points (x₁, y₁) and (x₂, y₂). This is essential for finding the perimeter of polygons on a coordinate...