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Complex Polygons: Concave, Convex, and Irregular Shapes

Solve problems that require manipulation and application of formulas related to perimeter, area, volume, capacity, Pythagorean theorem, trigonometric ratios, income, currency exchange, interest and finance charges

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Upper and lower bound

Upper and Lower Bound

Conversions between metric and imperial systems

Metric to Imperial Conversions

Imperial to Metric Conversions

Conversions Between Metric and Imperial Systems Speed KM to MI

Conversions Between Metric and Imperial Systems Speed  MI to M

Metric-Imperial Length Conversion Inch To Cm

Metric-Imperial Length Conversion MM/CM/M/KM To FT

Metric-Imperial Length Conversion MM/CM/M/KM To MI

Metric systems

Add and Subtract Mixed Units

Metric Length Conversion

Add or Subtract Different Metric Units Convert to CM

Add or Subtract Different Metric Units Convert to M

Add or Subtract Different Metric Units Convert to MM

Imperial systems

Imperial Length Conversion

Conversions involving squares and cubic

Imperial to Metric Conversions — Squares and Cubes

Imperial Conversion — Squares and Cubes

Metric to Imperial Conversion — Squares and Cubes

Metric Area Conversion FT to CM

Metric Area Conversion Foot to Inch

Metric Area Conversion M/CM to Inch

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Analyze puzzles and games that involve spatial reasoning, using problem-solving strategies

Patterns

Patterns — Word Problem

Evaluating algebraic expressions

Evaluating Algebraic Expressions

Solving one - step equations:  x + a = b

1-step Equations

1-step Equations — Word Problem

Demonstrate an understanding of the Pythagorean theorem

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Demonstrate an understanding of primary trigonometric ratios

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Use tangent ratio to calculate angles and sides (Tan = o / a)

Solve problems that involve angle relationships between parallel, perpendicular and transversal lines

Parallel and perpendicular lines in linear functions

Applications of linear relations

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Demonstrate an understanding of angles, including acute, right, obtuse, straight and reflex

Introduction to bearings

Bearings and direction word problems

Bearings and Direction Word Problems

Angle of elevation and depression

Triangles

Rectangles

Parallelograms

Trapezoids, rhombi, and kites

Polygons

Complex polygons

Solve problems that involve unit pricing and currency exchange, using proportional reasoning

Rate of change

Applications of rational equations

Converting repeating decimals to fractions

Demonstrate an understanding of income, including wages, salary, contracts, commissions, and piecework to calculate gross pay and net pay

Types of pay

Income & savings

Demonstrate an understanding of financial institution services used to access and manage finances

Bank account

Ordinary annuity

Budgeting

Demonstrate an understanding of simple and compound interest

Simple interest

Simple Interest — Word Problem

Basic Concepts of Simple Interest – Word Problem

Borrowing Money for More Than One Year  – Word Problem

Investigate the Advantages of Borrowing Money  – Word Problem

Compound inequalities

Analyze the Alternate Form of Compound Inequalities: AND

Compound linear inequalities

Evaluate Compound Inequalities: And

Applications of quadratic equations

Scientific notation

Demonstrate an understanding of credit options, including credit cards and loans

Taxes, discounts, tips and more

Discounts — Word Problem

Taxes — Word Problem

Percentage - Applying a Discount Price– Word Problem

Percentage - Applying a Discount Percent – Word Problem

Percentage - Applying a Tax Total – Word Problem

Percentage - Applying a tax Percent – Word Problem

Assignments

Challenge Zone

Foundation Review

Geometry, Measurement and Finance 10

Measurement

Number

math

This lesson explains complex polygons, focusing on the difference between convex and concave shapes such as concave pentagons, hexagons, and octagons, and walks through finding the area of an irregular polygon using triangle decomposition.

Area and perimeter of complex polygons

Complex Polygons | StudyPug

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Overview

Complex Polygons: Concave vs Convex Polygons

What You'll Learn

Identify a convex polygon by checking that every interior angle is less than 180 degrees

Recognize a concave polygon by spotting at least one reflex angle greater than 180 degrees

Compare concave pentagons, hexagons, and octagons using the same reflex-angle test regardless of side count

Apply triangle decomposition to calculate the area of an irregular or concave polygon

Subtract the area of a reflex notch when a diagonal of a concave shape falls outside the figure

Calculate total area by summing or subtracting the areas of simple shapes that make up a complex polygon

This Unit Includes

Learning resources