UNIT 6 Nets and Surface Area Overhead Slides Overhead Slides 6.1 Polygons 6.2 Triangles 6.3 Quadrilaterals 6.4 Name that Shape! 6.5 Drawing Parallelograms 6.6 3-D Shapes 6.7 Cuboid 6.8 Prism 6.9 Plan and Elevation of Garage 6.10 Plan and Elevation of Prism 6.11 Net of a Cube 6.12 Net of a Cuboid 6.13 Surface Area of Cube 6.14 Surface Area of Cuboid 6.15 Net of a Prism 6.16 Net of a Pyramid
OS 6.1 Polygons NAME ILLUSTRATION NOTES Triangle 3 straight sides Quadrilateral 4 straight sides Pentagon 5 sides (equal if regular) Hexagon 6 sides (equal if regular) Octagon 8 sides (equal if regular) Circle Symmetric about any diameter (an infinite number of sides)
OS 6.2 Triangles NAME ILLUSTRATION NOTES Triangle 3 straight sides Equilateral Triangle 3 equal sides and o 3 equal angles (= 60 ) Isosceles Triangle 2 equal sides and 2 equal angles Right-angled Triangle One angle = 90 o
OS 6.3 Quadrilaterals NAME ILLUSTRATION NOTES Quadrilateral 4 straight sides Square Rectangle Rhombus Trapezium Parallelogram Kite 4 equal sides and 4 right angles Opposite sides equal and 4 right angles 4 equal sides; opposite sides parallel One pair of opposite sides parallel Both pairs of opposite sides equal and parallel Two pairs of adjacent sides equal
OS 6.4 Name that Shape! Name each of the shapes shown below: 4 cm 4 cm A 5 cm 6 cm 6 cm 5 cm B 5 cm C 5 cm 6 cm 4 cm D 6 cm 4 cm E 40 F 4 cm 60 70 70 G 4 cm 60 H 60 I 4 cm J 5 cm 7 cm 7 cm K L 3 cm 3 cm
OS 6.5 Drawing Parallelograms Draw a parallelogram with sides of length 8 cm and 10 cm and angles of 140 and 40. The drawing has been started for you. 40 10 cm
OS 6.6 3-D Shapes NAME ILLUSTRATION NOTES Cube Cuboid All side lengths equal (square faces), and all angles right angles Faces are combination of rectangles (and, possibly, squares); all angles right angles Cylinder Circular base Sphere Pyramid Prism Tetrahedron All points on surface equidistant from centre All slant edges are equal in length in a right pyramid Cross-section remains the same throughout All four faces are triangular
OS 6.7 Cuboid A cuboid has sides of length 2 cm, 3 cm and 4 cm. The cuboid can be drawn in 3 different ways. Draw these on the isometric paper below.
OS 6.8 Prism Draw this prism on the isometric paper below: 5 cm 3 cm 4 cm
OS 6.9 Plan and Elevations of Garage Complete the plan and elevations of this garage: 4 m 3 m 6 m 4 m Scale: 1 small square represents 1 m SIDE ELEVATION PLAN FRONT ELEVATION
OS 6.10 Plan and Elevations of Prism Draw the plan and elevations of this prism: 4 cm Scale: 1 small square represents 1 m 3 cm 5 cm
OS 6.11 Net of a Cube Complete the following net of a cube: Now complete the net in a different way:
OS 6.12 Net of a Cuboid Part of the net of a cuboid has been drawn below. (a) Complete the net. Scale: 1 small square represents 1 m (b) Calculate the surface area of the cuboid.
OS 6.13 Surface Area of Cube The net of a cube is always made up of 6 identical squares. Each square has an area of x 2 when the length of the side of the cube is x. Total surface area of a cube = 6 2 x. x 2 x 2 x 2 x 2 x 2 folded gives x 2
OS 6.14 Surface Area of Cuboid The net of a cuboid is made up of 6 rectangles. The rectangles will occur in pairs as illustrated below: Top and bottom Two sides Two ends For the following cuboid, x y z unfolds to give yz xy yz and the surface area is: = xy+ yz + xz + xy+ yz + xz = 2xy+ 2yz + 2xz ( ) = 2 xy+ yz + xz xz xy xz
OS 6.15 Net of a Prism Part of the net of a prism has been drawn below. (a) Complete the net. Scale: 1 small square represents 1 m (b) Calculate the surface area of the prism.
OS 6.16 Net of a Pyramid The incomplete nets for two pyramids are shown below. Complete these nets.