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# Grades 9/10/11 Measurement, Geometry, and Trigonometry

Pythagorean Theorem. Measurement of 2D figures and 3D solids. Optimization. Geometric relationships. Triangle trigonometry. Angles in standard position and trigonometric identities.

This is one of seven strands of the CEMC Grade 9/10/11 courseware. The other strands and more information about this courseware is available on the Grade 9/10/11 homepage.

## Units

### Unit 1: The Pythagorean Theorem, Measurement, and Optimization

In this lesson, we make connections between the geometric and algebraic representations of the Pythagorean Theorem. We will use it to solve applications involving missing side lengths of right triangles and investigate the converse of the Pythagorean Theorem.

In this lesson, we make connections between complex and simple two-dimensional shapes to solve applications involving the perimeter and area of composite shapes.

In this lesson, we will make connections between the net and the surface area of pyramids and cones. We will use different strategies to solve surface area applications.

We continue our exploration of pyramids and cones making connections about their volumes with those of prisms and cylinders. We will solve problems involving the volume of pyramids and cones within different contexts.

In this lesson, we will work with the formulas for the volume and surface area of a sphere to solve application problems.

In this lesson, we will explore how rectangles with the same perimeter may have different areas. We will develop strategies and tools to determine the maximum area of rectangles with a fixed perimeter in different settings.

In this lesson, we will explore how rectangles with the same area may have different perimeters. We deepen our understanding of strategies and tools used for mathematical optimization to determine the minimum perimeter for rectangles with a fixed area.

Conservation of materials and heat are some of the applications of minimizing the surface area of 3D objects. In this lesson, we will make connections between the dimensions and surface area of cylinders and square-based prisms using different strategies to find the optimal shape.

This last optimization lesson makes connections between cylinders and square-based prisms with a fixed surface area and its shape when the volume is maximized.

All of the pencil and paper practice exercises, answers, and solutions for this unit are reproduced here.

This is a collection of additional, and sometimes challenging, problems that extend the material covered in this unit, connect material from different lessons, and further explore real-world applications.