Question

make some notes that could look like a high schooler did them from these topics

Attributes of Rectangular Prisms and Pyramids
Surface Area of Right Rectangular Prisms
Surface Area of Pyramids
Volume of Right Rectangular
Volume of Pyramids
Right Rectangular Prisms & Pyramids

Answer 1

### Attributes of Rectangular Prisms and Pyramids

**Rectangular Prism:**
- Definition: A 3D shape with 6 rectangular faces.
- Faces: 6 (all rectangles)
- Edges: 12
- Vertices: 8
- Must have right angles.

**Pyramid:**
- Definition: A 3D shape with a polygonal base and triangular faces that meet at a point (apex).
- Faces: 1 base + triangles = total faces.
- Edges: Base edges + triangular edges.
- Vertices: Base vertices + apex.
- Types: Regular (base is a regular polygon) and irregular.

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### Surface Area of Right Rectangular Prisms

**Formula:**
- SA = 2lw + 2lh + 2wh
- l = length
- w = width
- h = height

**Steps to Calculate:**
1. Find the area of each rectangle (2 of each pair).
2. Add all areas together for total surface area.

**Example:**
- l = 3, w = 4, h = 5
SA = 2(3*4) + 2(3*5) + 2(4*5)
= 24 + 30 + 40 = 94 units²

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### Surface Area of Pyramids

**Formula:**
- SA = Base Area + (1/2 * Perimeter of Base * Slant Height)

**Steps to Calculate:**
1. Calculate the area of the base.
2. Find the perimeter of the base.
3. Use slant height for the triangular faces.

**Example:**
- Base = square: side = 4
Base Area = 4² = 16
Perimeter = 4 sides × 4 = 16
Slant height = 5
SA = 16 + (1/2 * 16 * 5) = 16 + 40 = 56 units²

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### Volume of Right Rectangular Prisms

**Formula:**
- Volume = l * w * h

**Example:**
- l = 3, w = 4, h = 5
Volume = 3 * 4 * 5 = 60 units³

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### Volume of Pyramids

**Formula:**
- Volume = (1/3) * Base Area * Height

**Example:**
- Base = square: side = 4, height = 6
Base Area = 4² = 16
Volume = (1/3) * 16 * 6 = 32 units³

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### Right Rectangular Prisms & Pyramids Recap

**Right Rectangular Prisms:**
- Consistent dimensions, rectangular faces.
- Easy to calculate area and volume.

**Pyramids:**
- Vary with base shape.
- Use slant height for surface area.
- Volume relies on the base area and height.

### Study Tips:
- Practice calculating surface area and volume with different dimensions.
- Remember the difference between surface area (2D) and volume (3D).
- Draw diagrams to visualize shapes.