Prism Surface Area and Volume
Year 11 Mathematics Using the Perimeter Method Building 3D Understanding
What Do You Already Know?
Think about 3D shapes around you What makes a prism different from other 3D shapes? Can you name the parts of a prism?
What is a Prism?
A 3D shape with two parallel, congruent faces (bases) Connected by rectangular faces Cross-section remains constant along its length Examples: triangular, rectangular, pentagonal prisms
Prism Identification Challenge
Work in pairs Sort the 3D shapes provided Identify which are prisms and which are not Explain your reasoning to your partner
Key Vocabulary
Base: The parallel, congruent faces Height: Distance between the bases Lateral faces: Rectangular faces connecting bases Edge: Where two faces meet Vertex: Where edges meet
Why the Perimeter Method Works
Lateral surface area = Perimeter × Height Think of 'wrapping' the prism sides Base areas are added separately (2 × base area) Formula: SA = P × h + 2A
Guided Practice: Triangular Prism
Given: Triangle base with sides 3cm, 4cm, 5cm Height of prism: 8cm Step 1: Find perimeter of base Step 2: Calculate base area Step 3: Apply the formula
Worked Example Solution
{"left":"Step 1: Perimeter = 3 + 4 + 5 = 12cm\nStep 2: Base area = ½ × 3 × 4 = 6cm²","right":"Step 3: SA = P × h + 2A\nSA = 12 × 8 + 2 × 6 = 108cm²"}
Volume of Prisms
Volume = Base Area × Height V = A × h Works for any prism shape Units are always cubic (cm³, m³, etc.)
Volume Practice
Calculate volume for the same triangular prism Base area = 6cm² Height = 8cm Show your working Compare with a partner
Real-World Applications
Where do we use these calculations in real life? Think about: Architecture and construction Packaging and shipping Manufacturing and design
Design Challenge
Design a gift box (rectangular prism) Volume must be exactly 200cm³ Minimize surface area to save material Present your solution to the class
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