Unit 08 · Area Volume and Surface AreaLesson

Day 119Choosing Area Volume or Surface Area

LearnClassworkAnswer keyPDF packet ↗
Standards 6.G.A.16.G.A.26.G.A.4
LEARNING TARGET

I can choose the correct geometric measure and justify the units.

Build the idea

Read the requested quantity first and identify the relevant model. Two matching triangles form a parallelogram, so A = (base × perpendicular height)/2. A slanted side is not necessarily the height. Label area in square units. Explain why the units and the final value fit the situation.

WORKED EXAMPLE 1

A rectangular prism has edges 3, 1 1/2, and 6 cm. Sketch it and find its volume.

27 cm³

B = 3 × 3/2 = 9/2 cm²; V = B × 6 = 27 cm³.

WORKED EXAMPLE 2

A 3 cm by 5 cm base and 4 cm height form an open-top box. Draw its net and find the material area. Ignore tabs and overlap.

79 cm²

Closed surface area = 2(15+12+20) = 94. Remove the top area 15: 79.

Your turn

Work in order. Start with the foundations, then build toward explanation and application.

  1. Sketch a triangle with base 16 cm and perpendicular height 3 cm. Find its area.

  2. A rectangular prism has edges 6, 1, and 5 cm. Sketch it and find its volume.

  3. A 6 cm by 2 cm base and 2 cm height form a closed box. Draw its net and find the material area. Ignore tabs and overlap.

  4. An L-shaped garden is a 11 m by 11 m rectangle with an 7 m by 7 m corner rectangle removed. Sketch and find the garden area.

  5. A square pyramid has base edge 8 cm. Each triangular face has perpendicular face height 7 cm. Draw a net and calculate total surface area.

  6. Sketch a triangle with base 8 cm and perpendicular height 2 cm. Find its area.

  7. A rectangular prism has edges 2 1/2, 2 1/2, and 3 cm. Sketch it and find its volume. Show both lwh and Bh.

  8. A 4 cm by 7 cm base and 3 cm height form an open-top box. Draw its net and find the material area. Ignore tabs and overlap.

  9. A 11 m by 7 m rectangle has a right-triangle corner removed with perpendicular legs 3 m and 4 m. Sketch the remaining polygon and find its area.

  10. A square pyramid has base edge 14 cm. Each triangular face has perpendicular face height 10 cm. Draw a net and calculate total surface area. Explain why the vertical pyramid height is not needed.

Answers and reasoning

Reveal the teacher answer key
  1. 24 cm²

    A = bh/2 = 16 × 3 ÷ 2 = 24. Two such triangles make a parallelogram.

  2. 30 cm³

    B = 6 × 1 = 6 cm²; V = B × 5 = 30 cm³.

  3. 56 cm²

    Closed surface area = 2(12+12+4) = 56.

  4. 72 m²

    Outer area 121 minus cutout 49 = 72.

  5. 176 cm²

    Base = 64; each triangle = 8 × 7 ÷ 2 = 28; add four triangles to get 176.

  6. 8 cm²

    A = bh/2 = 8 × 2 ÷ 2 = 8. Two such triangles make a parallelogram.

  7. 75/4 cm³

    B = 5/2 × 5/2 = 25/4 cm²; V = B × 3 = 75/4 cm³.

  8. 94 cm²

    Closed surface area = 2(28+12+21) = 122. Remove the top area 28: 94.

  9. 71 m²

    Whole rectangle 77; remove triangle 6; difference 71.

  10. 476 cm²

    Base = 196; each triangle = 14 × 10 ÷ 2 = 70; add four triangles to get 476.

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