By Saul Stahl
Tracing the formal improvement of Euclidean geometry, this article heavily follows Euclid's vintage, Elements. as well as supplying a old point of view on airplane geometry, it covers comparable themes, together with non-neutral Euclidean geometry, circles and typical polygons, projective geometry, symmetries, inversions, knots and hyperlinks, and casual topology. comprises 1,000 perform difficulties. suggestions to be had. 2003 variation.
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Extra resources for Geometry from Euclid to Knots
Example text
5 in. 3 in. 2 in. 13 ft 9m 7m 5. 5m 3m 6. 5m 4m 7m 7. 10 in. 6 cm 8 in. 13 m 3 cm 3m 9. 8. 3 in. 5m 7m 6 cm 3 cm 10. 17 ft 5 cm 46 ft 2 2 40 m 9 cm 2 72 in. 2 20 in. 3 ft 8 ft 100 ft 5 in. 11. 12. 10 ft 2 42 cm 2 2 32 in. 2 240 cm 138 m 2 2 13 ft 81 m 13 ft 2 in. 144 m 5 in. 165 ft 20 ft © Milliken Publishing Company 29 180 ft 2 36 cm 2 2 2 2 8 in. MP3497 Name _________________________________ Surface Area of Right Prisms Remember 1. A right prism is a solid with two parallel, congruent polygons for bases and rectangles for lateral faces.
The height must be perpendicular to the base. 4 3 3 8 6 base2 Parallelogram: A = bh Trapezoid: A = Area = base x height Area = 2 A = 6 · 3 = 18 units A= 1 2 1 2 1 2 h(b1 + b2) x height x (base1 + base2) · 3 · (4 + 8) = 1 2 2 · 3 · 12 = 18 units Find the area of these parallelograms and trapezoids. Then shade in your answers. 1. 2. 24 cm 10 cm 14 m 3. 10 ft 4 ft 4. 13 m 12 m 1 in. 5 in. 3 in. 2 in. 13 ft 9m 7m 5. 5m 3m 6. 5m 4m 7m 7. 10 in. 6 cm 8 in. 13 m 3 cm 3m 9. 8. 3 in. 5m 7m 6 cm 3 cm 10.
10 in. 6 cm 8 in. 13 m 3 cm 3m 9. 8. 3 in. 5m 7m 6 cm 3 cm 10. 17 ft 5 cm 46 ft 2 2 40 m 9 cm 2 72 in. 2 20 in. 3 ft 8 ft 100 ft 5 in. 11. 12. 10 ft 2 42 cm 2 2 32 in. 2 240 cm 138 m 2 2 13 ft 81 m 13 ft 2 in. 144 m 5 in. 165 ft 20 ft © Milliken Publishing Company 29 180 ft 2 36 cm 2 2 2 2 8 in. MP3497 Name _________________________________ Surface Area of Right Prisms Remember 1. A right prism is a solid with two parallel, congruent polygons for bases and rectangles for lateral faces. 2. To find the surface area (SA) of any right prism, add the area of the two bases (2B) and the area of all the lateral faces (LA).