Mastering Surface Area of 3D Figures: Nets and Real-World Applications
This lesson focuses on understanding surface area through the use of nets for three-dimensional figures, including cubes, prisms, and pyramids. Students will learn how to represent these shapes using nets made of rectangles and triangles, enabling them to calculate surface area by summing the areas of all faces. The course also emphasizes applying geometric concepts to real-world problems, enhancing problem-solving skills and vocabulary in geometry.
Mastering Surface Area of 3D Figures: Nets and Real-World Applications
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Presentation Transcript
Finding Surface Area Math 6
Objectives 1- Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. 2- Apply these techniques in the context of solving real-world and mathematical problems.
Geometric Shapes Polygons Polyhedra (Polyhedrons) solid figures (3-dimensional) Faces are polygons Edges are line segments • Plane (flat) closed figures. • Sides are line segments.
Solid (3-Dimensional) Geometric Shapes
Cube A net is a two-dimensional representation of a three-dimensional figure.
How to Find Surface Area • Find the area of each face. • Add them all together.
Nets of pyramids Nets of pyramids
We can describe nets and their solids by the number of: edges vertices faces. Solids include rectangular and triangular prisms
Here is a website which might be helpful. http://illuminations.nctm.org/ActivityDetail.aspx?ID=205
Keys to Geometry Master the vocabulary • Polygon • Parallel • Perimeter • Perpendicular • Area • Rectangle • Right angle • Line segments
Keys to Geometry Master the vocabulary • Polygon • Trapezoid • rhombus • parallelogram • Complex figure • Regular polygon
Online Math Dictionaries http://www.mathsisfun.com/definitions/letter-a.html http://www.icoachmath.com/math_dictionary/mathdictionarymain.html#P http://my.hrw.com/math06_07/nsmedia/tools/glossary/msm/glossary.html
Guided Practice 1 The figure is a cube. Find the surface area.
Guided Practice 2 The figure is a triangular prism. Find the surface area.
Guided Practice 3 The figure is a pyramid with a square base. Find the surface area.
Guided Practice 4 The figure is a pyramid with a triangular base. Find the surface area.
Conclusion • Surface Area of a solid means the amount of space on the surface. • It is a measure of area, thus the units are square units. • We can find surface area of prisms and pyramids by finding the area of each face and adding. • A net can be helpful to use.
Assignment Find the surface area of solids. • Solve the practice exercises on the attached page. Show all work.
"No employment can be managed without arithmetic, no mechanical invention without geometry." ~Benjamin Franklin
