United University

Geometry Grade 11. Polyhedra. Collection 1

Course Difficulty Icon Intermediate
Course Type Icon Course
Course Duration Icon 14 hours

This interactive course introduces 11th-grade students to the study of polyhedra and their properties. Learners explore prisms, parallelepipeds, pyramids, and regular polyhedra through engaging lessons, problem-solving tasks, and self-assessment activities. All topic-based tests are fully interactive, making learning dynamic and effective. The course develops spatial imagination, geometric visualization, and analytical thinking, helping students confidently apply solid geometry concepts in practical and theoretical contexts.

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This interactive course introduces 11th-grade students to the fascinating world of polyhedra. It provides a structured and engaging exploration of three-dimensional figures, their properties, and relationships. Students will study prisms, parallelepipeds, pyramids, and regular polyhedra through theoretical lessons, practical tasks, and competence-based tests. The course promotes spatial imagination and analytical thinking through problem-solving and independent practice.

Key Features of the Course

  • Interactive and structured learning with problem-solving activities
  • Development of spatial reasoning and geometric visualization
  • Comprehensive coverage of polyhedra and their key properties
  • Exercises designed for both classroom practice and self-study
  • Aligned with the national curriculum standards in mathematics

Course Modules

Module 1: Polyhedra

  • Introduction
  • Welcome message to 11th-grade students
    Lesson 1: Dihedral and Polyhedral Angles. Polyhedron. Prism
  • Solve problems and complete exercises 1.1 – 1.25
  • Solve problems and complete exercises 1.26 – 1.50
  • Solve problems and complete exercises 1.51 – 1.75
  • Solve problems and complete exercises 1.76 – 1.100
  • Solve problems and complete exercises 1.101 – 1.122
  • Test your competence
    Lesson 2: Parallelepiped
  • Solve problems and complete exercises 2.1 – 2.25
  • Solve problems and complete exercises 2.26 – 2.50
  • Solve problems and complete exercises 2.51 – 2.75
  • Solve problems and complete exercises 2.76 – 2.107
  • Test your competence
    Lesson 3: Pyramid
  • Solve problems and complete exercises 3.1 – 3.25
  • Solve problems and complete exercises 3.26 – 3.50
  • Solve problems and complete exercises 3.51 – 3.75
  • Solve problems and complete exercises 3.76 – 3.100
  • Solve problems and complete exercises 3.101 – 3.125
  • Solve problems and complete exercises 3.126 – 3.141
  • Test your competence
    Lesson 4: Regular Polyhedra
  • Solve problems and complete exercises 4.1 – 4.25
  • Solve problems and complete exercises 4.26 – 4.43
  • Test your competence
  • Independent Homework #1
  • Knowledge review tasks for §§ 1–4
  • Review exercises for Section 1
  • For §1
  • For §2
  • For §3
  • For §4

Expected Learning Outcomes

  • Recognizes the main types of polyhedra and their elements.
  • Illustrates basic types of polyhedra and identifies their components.
  • Understands the concept of a cross-section of a polyhedron by a plane.
  • Formulates definitions of studied polyhedra and their properties.
  • Writes formulas for calculating the lateral and total surface area of prisms and pyramids.
  • Calculates measures of key elements of polyhedra.
  • Applies formulas and properties to solve problems, including applied ones.

This course builds upon geometric knowledge by deepening students’ understanding of three-dimensional shapes. Through practice, visualization, and reasoning, learners will gain the skills to model spatial forms, perform accurate geometric constructions, and solve complex problems in solid geometry.

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