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Grade 6 · Mathematics · 30 minutes

Unit 2 · Expressions, equations and shape · Lesson 2 of 2

Triangle Area and a Box Net

Decompose a triangle and unfold a box to keep area measures meaningful.

Mr. S Teaches · Original starter mini-lesson · MS6-MATH-05

Learning objective

Calculate a triangle’s area and use a net to find the surface area of a rectangular box.

Before you begin

  • Rectangle area
  • Multiplication
  • Perpendicular lines

Gather your materials

  • Grid paper and pencil
  • Ruler
  • Optional paper box or adult-prepared net

Language to know

height
A perpendicular distance from a base to the opposite point or face.
net
A flat arrangement of faces that folds into a solid.
surface area
The total area of a solid’s outer faces.

Understand the concept

A triangle has half the area of a rectangle or parallelogram with the same base and perpendicular height. A slanted side is not automatically the height. Surface area counts the square units covering all faces; volume counts cubic units inside. A net helps account for each face exactly once.

Teach it step by step

  1. Draw a 6-by-4 rectangle and divide it diagonally into two equal-area triangles.
  2. Label the triangle’s base 6 cm and its perpendicular height 4 cm, then derive half of 6 × 4.
  3. Sketch six faces of a 4-by-3-by-2 cm box: two 4×3, two 4×2 and two 3×2 rectangles.
  4. Label matching opposite faces before adding their areas.
  5. Ask learners to explain why surface area uses square centimeters and not cubic centimeters.

Make the thinking visible

Worked example or model response

Triangle: (6 × 4)/2 = 12 cm². Box net: 2(4×3) + 2(4×2) + 2(3×2) = 24 + 16 + 12 = 52 cm². The calculation counts the six faces without double counting.

Guided practice

Calculate a triangle with base 8 cm and height 5 cm. Together draw and label a net for a cube with side 3 cm.

Independent practice

1. Find the area of a triangle with base 10 m and perpendicular height 7 m. 2. Find the surface area of a 5×2×2 cm box. List each face pair.

Quick assessment

Can a triangle’s 9 cm slanted side replace a 6 cm perpendicular height in its area formula? Explain.

Answer key & assessment criteria

Answers and teaching guidance

  1. Guided: Triangle area 20 cm². Cube net has six 3×3 faces; total 54 cm².
  2. Independent 1: 35 m². 2: 2(5×2) + 2(5×2) + 2(2×2) = 48 cm².
  3. Quick check: No. The formula requires perpendicular height, not an arbitrary side length.

Look for: Look for an explanation of the choices, not only a final answer. Require units and a check against the context.

Make it work for your learner

More support

Fold or trace paper rectangles; color opposite box faces with matching colors.

Extension challenge

Design two rectangular boxes with the same volume but different surface areas.

Selected contributions · Official sources

Standards connections

Contributes to Common Core standard

6.G.A.1

Common Core · Grade 6

Find triangle area by decomposing or composing familiar shapes.

Read the official standard ↗

This lesson contributes selected skills; it does not fully address the standard.

Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.

Contributes to Common Core standard

6.G.A.4

Common Core · Grade 6

Represent a box with a rectangular net and calculate its surface area.

Read the official standard ↗

This lesson contributes selected skills; it does not fully address the standard.

Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.