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Reveal Math · Unit 5 · Supplemental

Geometry & Measurement

Grade 6 · Standards 6.G.A.1 (area), 6.G.A.2 (volume), 6.G.A.4 (surface area)

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Word Bank

▱Parallelogram — a 4-sided shape with both pairs of sides parallel.
🔺Triangle — a 3-sided shape.
⬛Rectangular prism — a box shape with 6 rectangle faces.
📐Area — how much surface a flat shape covers (square units).
📦Volume — how much space a solid fills (cubic units).
🎁Surface area — the total area of all the outside faces.
Formulas: Rectangle area = length × width  ·  Parallelogram area = base × height  ·  Triangle area = ½ × base × height  ·  Prism volume = length × width × height.

Worked Example

Find the area of a triangle with base 8 and height 5

Step 1: Write the formula: Area = ½ × base × height.
Step 2: Multiply base × height: 8 × 5 = 40.
Step 3: Take half: 40 ÷ 2 = 20.
Answer: area = 20 square units.

Sentence Frames

The area of the rectangle is because I multiplied by .
Area is measured in units; volume is measured in units.
To find the volume, I multiply × × .

Guided Practice

Directions: Solve each problem. Show your work and write the correct units. Use the hint cue if you need help.
  1. Find the area of a rectangle 7 cm long and 4 cm wide.
    Hint: area = length × width.
  2. Find the area of a parallelogram with base 9 in and height 6 in.
    Hint: area = base × height.
  3. Find the area of a triangle with base 10 ft and height 4 ft.
    Hint: ½ × base × height.
  4. Find the area of a triangle with base 6 m and height 7 m.
    Hint: multiply 6 × 7, then take half.
  5. Find the volume of a box 3 cm × 4 cm × 5 cm.
    Hint: multiply all three dimensions.
  6. Find the volume of a cube with edges of 4 in.
    Hint: 4 × 4 × 4.
  7. A rectangular prism is 2 m × 2 m × 6 m. Find the volume.
    Hint: 2 × 2 × 6.
  8. Find the surface area of a cube with edges of 3 cm.
    Hint: one face is 3 × 3 = 9. A cube has 6 faces.
  9. A net shows 6 squares, each 5 in × 5 in. What is the total surface area?
    Hint: area of one square × 6.
  10. A garden bed is a rectangle 8 ft by 3 ft. How much soil area must be covered?
    Hint: this is just rectangle area.

Answer Key

  1. 7 × 4 = 28 cm².
  2. 9 × 6 = 54 in².
  3. ½ × 10 × 4 = 20 ft².
  4. ½ × 6 × 7 = 21 m².
  5. 3 × 4 × 5 = 60 cm³.
  6. 4 × 4 × 4 = 64 in³.
  7. 2 × 2 × 6 = 24 m³.
  8. 6 × (3 × 3) = 54 cm².
  9. 6 × (5 × 5) = 150 in².
  10. 8 × 3 = 24 ft².