Sketch a triangle with base 4 cm and perpendicular height 4 cm. Find its area.
8 cm²
A = bh/2 = 4 × 4 ÷ 2 = 8. Two such triangles make a parallelogram.
Day 106Triangle Areas by Decomposition
Standards 6.G.A.1
LEARNING TARGET
I can find the area of any triangle using a perpendicular height.
01 · LEARN
Build the idea
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.
Sketch a triangle with base 16 cm and perpendicular height 3 cm. Find its area. Explain why the slanted side is not needed.
24 cm²
A = bh/2 = 16 × 3 ÷ 2 = 24. Two such triangles make a parallelogram.
02 · PRACTICE
Your turn
Work in order. Start with the foundations, then build toward explanation and application.
Sketch a triangle with base 6 cm and perpendicular height 2 cm. Find its area.
Sketch a triangle with base 12 cm and perpendicular height 6 cm. Find its area.
Sketch a triangle with base 10 cm and perpendicular height 3 cm. Find its area.
Sketch a triangle with base 4 cm and perpendicular height 5 cm. Find its area.
Sketch a triangle with base 4 cm and perpendicular height 2 cm. Find its area.
Sketch a triangle with base 14 cm and perpendicular height 6 cm. Find its area.
Sketch a triangle with base 6 cm and perpendicular height 3 cm. Find its area. Explain why the slanted side is not needed.
Sketch a triangle with base 4 cm and perpendicular height 2 cm. Find its area. Explain why the slanted side is not needed.
Sketch a triangle with base 12 cm and perpendicular height 2 cm. Find its area. Explain why the slanted side is not needed.
Sketch a triangle with base 12 cm and perpendicular height 3 cm. Find its area. Explain why the slanted side is not needed.
03 · CHECK
Answers and reasoning
Reveal the teacher answer key
- 6 cm²
A = bh/2 = 6 × 2 ÷ 2 = 6. Two such triangles make a parallelogram.
- 36 cm²
A = bh/2 = 12 × 6 ÷ 2 = 36. Two such triangles make a parallelogram.
- 15 cm²
A = bh/2 = 10 × 3 ÷ 2 = 15. Two such triangles make a parallelogram.
- 10 cm²
A = bh/2 = 4 × 5 ÷ 2 = 10. Two such triangles make a parallelogram.
- 4 cm²
A = bh/2 = 4 × 2 ÷ 2 = 4. Two such triangles make a parallelogram.
- 42 cm²
A = bh/2 = 14 × 6 ÷ 2 = 42. Two such triangles make a parallelogram.
- 9 cm²
A = bh/2 = 6 × 3 ÷ 2 = 9. Two such triangles make a parallelogram.
- 4 cm²
A = bh/2 = 4 × 2 ÷ 2 = 4. Two such triangles make a parallelogram.
- 12 cm²
A = bh/2 = 12 × 2 ÷ 2 = 12. Two such triangles make a parallelogram.
- 18 cm²
A = bh/2 = 12 × 3 ÷ 2 = 18. Two such triangles make a parallelogram.