• Mathematics General
• Year 11

# Shape and Measurement

approx. 15 hrs

7 topics

40 concepts

Enrol in Shape and Measurement to optimise your academic outcomes in Mathematics.

Available in
ACT NT QLD SA TAS VIC WA

### Overview

Shape and Measurement will extend the knowledge and skills of similarity and associated calculations involving simple and compound geometric shapes. We will help students effectively apply these skills in a range of practical contexts, including those involving three-dimensional shapes.

### Topics & Concepts We Cover

This learning program is made up of the following 7 topics, broken down into 40 concepts.

• #### Application of Pythagoras Theorem 2 concepts

1. Review Pythagoras theorem

2. Apply Pythagoras' Theorem to 3D problems

• #### Calculating Perimeter 5 concepts

1. Develop and use the formulas to find the circumferences of circles in terms of the diameter or radius

2. Find the perimeters of composite figures including sectors

3. Use formulae to find the arc length of a sector

4. Find the perimeter of sectors including quadrants and semicircles

5. Find the perimeters of a range of plane shapes, including composite figures

• #### Calculating Area 4 concepts

1. Finding the area of a triangle using Heron’s formula

2. Review area of triangles, quadrilaterals, circles and sectors

3. Calculate the areas of composite figures by dissection into triangles, special quadrilaterals, quadrants, semicircles and sectors

4. Calculate the area of an annulus

• #### Volume of 3D Shapes 7 concepts

1. Calculate the volume of composite solids including right cones, hemispheres and right pyramids

2. Calculate the volume of a sphere

3. Calculate the volume of of right pyramids

4. Calculate the volume of a cone

5. Calculate the volume of an annular cylinder

6. Develop and use the formula for the volume of cylinders and find the capacity

7. Develop and use the formula for the volume of right prisms and find the capacity

• #### Surface Area of Right Prisms 8 concepts

1. Surface area of composite objects

2. Solve problems involving rectangular or triangular prisms

3. Find the surface area of a hollow cylinder

4. Apply Pythagoras' theorem to find surface areas of triangular prisms

5. Use the nets of prisms to find surface area

6. Find the surface areas of triangular prisms

7. Find the surface area of a cylinder

8. Find the surface area of rectangular prisms

• #### Surface Area of Right Cones, Pyramids and Spheres 5 concepts

1. Calculate the 'perpendicular heights' and 'slant heights' of right pyramids and right cones

2. Calculate the surface area of composite solids including right cones, hemispheres and right pyramids

3. Surface areas of right cones

4. Calculate the surface area of right pyramids

5. Surface areas of spheres

• #### Application of Similarity 9 concepts

1. Determine similar solids

2. Scaling problems involving volume and surface area

3. Name the matching sides and angles of similar figures

4. Investigate the minimum conditions needed for two triangles to be similar

5. Scaling ratio for volume

6. Scaling ratio for area

7. Tests for similar triangles

8. Determine the scale factor of two similar figures

9. Use a scale factor to find unknown sides

### What you'll get Learning Content

• A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
• All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions An Expert Tutor

• We match you to a private, expert tutor who is right for your needs and goals
• Our tutors are talented, tested, top ATAR achievers and subject experts
• During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Shape and Measurement Reporting

• Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
• You and your parents receive a comprehensive feedback report after every session
• Every session is recorded and available for you to watch at any time, allowing you to review what was covered

### Ready to start this program? Simply pick a time that works for you  We'll be in contact to match you with one of our top tutors and book your first session

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime