Perimeter

Learning Objectives Calculate the perimeter of complex composite figures by summing the lengths of their exterior sides. Apply the Pythagorean theorem to determine unknown side lengths required for perimeter calculations. Utilize trigonometric ratios (SOH CAH TOA) to find missing side lengths of polygons for perimeter calculations. Calculate the circumference of circles and the perimeter of sectors and composite shapes involving arcs. Solve multi-step, real-world problems involving perimeter, translating verbal descriptions into geometric models. Distinguish between perimeter and area and select the correct measurement for a given problem context. Planning to build a fence around a uniquely shaped garden or frame a custom piece of art? 🖼️ You'll need to master perimeter...

TermDefinitionExample PerimeterThe total continuous length of the boundary of a closed two-dimensional figure. It is a measure of the distance around the outside of a shape.For a rectangle with sides of 5 cm and 3 cm, the perimeter is 5 + 3 + 5 + 3 = 16 cm. CircumferenceThe specific term for the perimeter of a circle or an ellipse.A circle with a radius of 10 meters has a circumference of 2 * π * 10 ≈ 62.83 meters. Arc LengthThe distance along a section of the circumference of a circle. It is a portion of the total perimeter of the circle.For a circle with a radius of 4 cm, the length of an arc subtended by a 90° angle is (90/360) * 2 * π * 4 = 2π cm. Composite FigureA two-dimensional shape made from two or more basic geometric shapes (like rectangles, triangles, and circles) joined toget...

Perimeter of a Polygon P = s_1 + s_2 + s_3 + ... + s_n The perimeter of any polygon is the sum of the lengths of all its sides. For a regular n-sided polygon with side length 's', the formula simplifies to P = n * s. Circumference of a Circle C = 2 * \pi * r or C = \pi * d Use this formula to find the perimeter of a full circle, where 'r' is the radius and 'd' is the diameter. Arc Length Formula (Degrees) L = (\theta / 360) * 2 * \pi * r Use this to find the length of a part of a circle's circumference, where 'θ' is the central angle of the arc in degrees and 'r' is the radius. Pythagorean Theorem a^2 + b^2 = c^2 In a right-angled triangle, this theorem is used to find the length of an unknown side when...