UNIT 6 Nets and Surface Area Overhead Slides

Transcription

1 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 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

2 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)

3 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

4 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

5 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 G 4 cm 60 H 60 I 4 cm J 5 cm 7 cm 7 cm K L 3 cm 3 cm

6 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 cm

7 OS 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

8 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.

9 OS 6.8 Prism Draw this prism on the isometric paper below: 5 cm 3 cm 4 cm

10 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

11 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

12 OS 6.11 Net of a Cube Complete the following net of a cube: Now complete the net in a different way:

13 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.

14 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

15 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

16 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.

17 OS 6.16 Net of a Pyramid The incomplete nets for two pyramids are shown below. Complete these nets.