1. Algebra 1 Predicting Patterns & Examining Experiments Unit 6: Around the Plane Section 4: Fill ‘er Up

2. What’s the Area of this Shape? The shape is an equilateral triangle on top of a square. Per.=30. The shape is an equilateral triangle on top of a square. Per.=30. 66 66 6

3. What’s the Area of this Shape? The shape is an equilateral triangle on top of a square. Per.=30. The shape is an equilateral triangle on top of a square. Per.=30. 66 66 6 Area of the Square = Area of the Triangle = Area of the Square = Area of the Triangle =

4. What’s the Area of this Shape? The shape is an equilateral triangle on top of a square. Per.=30. The shape is an equilateral triangle on top of a square. Per.=30. 66 66 6 Area of the Square = Area of the Triangle = Area of the Square = Area of the Triangle = height

5. What’s the Area of this Shape? The shape is an equilateral triangle on top of a square. Per.=30. The shape is an equilateral triangle on top of a square. Per.=30. 66 66 6 Area of the Square = Area of the Triangle = Area of the Square = Area of the Triangle = height We are going to look at half of the equilateral triangle. We are going to look at half of the equilateral triangle. height 6 3

6. What’s the Area of this Shape? The shape is an equilateral triangle on top of a square. Per.=30. The shape is an equilateral triangle on top of a square. Per.=30. 66 66 6 Area of the Square = Area of the Triangle = Area of the Square = Area of the Triangle = height We are going to look at half of the equilateral triangle. We are going to look at half of the equilateral triangle. height 6 3

7. What’s the Area of this Shape? The shape is an equilateral triangle on top of a square. Per.=30. The shape is an equilateral triangle on top of a square. Per.=30. 66 66 6 Area of the Square = Area of the Triangle = Area of the Square = Area of the Triangle = height We are going to look at half of the equilateral triangle. We are going to look at half of the equilateral triangle. height 6 3

8. What’s the Area of this Shape? The shape is an equilateral triangle on top of a square. Per.=30. The shape is an equilateral triangle on top of a square. Per.=30. 66 66 6 Area of the Square = Area of the Triangle = Area of the Square = Area of the Triangle = height

9. What’s the Area of this Shape? The shape is an equilateral triangle on top of a square. Per.=30. The shape is an equilateral triangle on top of a square. Per.=30. 66 66 6 Area of the Square = Area of the Triangle = Total Area: 36 + 3√27 ≈ 51.588 Area of the Square = Area of the Triangle = Total Area: 36 + 3√27 ≈ 51.588 height

10. What is the Area of this Shape? 17 6 Perimeter = 6 + 17 + √98 + √65 ≈ 40.962 √98 √65

11. What is the Area of this Shape? 17 6 Perimeter = 6 + 17 + √98 + √65 ≈ 40.962 √98 √65 7 7 4 7 Remember:

12. What is the Area of this Shape? 17 6 Perimeter = 6 + 17 + √98 + √65 ≈ 40.962 √98 √65 7 7 4 7 Area: 47/2=14

13. What is the Area of this Shape? 17 6 Perimeter = 6 + 17 + √98 + √65 ≈ 40.962 √98 √65 7 7 4 7 Area: 47/2=14 Area: 67 = 42 7

14. What is the Area of this Shape? 17 6 Perimeter = 6 + 17 + √98 + √65 ≈ 40.962 √98 √65 7 7 4 7 Area: 47/2=14 Area: 67 = 42 Area:77/2=24.5 7

15. What is the Area of this Shape? 17 6 Perimeter = 6 + 17 + √98 + √65 ≈ 40.962 √98 √65 7 7 4 7 Area: 47/2=14 Area: 67 = 42 Area:77/2=24.5 Total Area: 80.5 7

16. Why can’t we add a fifth?

17. It is possible to fit four 3-4-5 triangles inside of a 5by5 square, but not a fifth. Complete a drawing with the four inside and explain why the fifth cannot be added.

18. Why can’t we add a fifth? It is possible to fit four 3-4-5 triangles inside of a 5by5 square, but not a fifth. Complete a drawing with the four inside and explain why the fifth cannot be added. The area of the square is 25 square units, and the area of each triangle is 34/2=6 square units. Therefore, there can be at most four triangles, because 46=24, but 56=30 > 25.

19. Disclaimer All photos contained are used under creative commons rights. Saltzman House by tantrum_dan http://www.flickr.com/photos/tantrum_dan/3172178310/