MISSION 1 THE PYRAMIDS OF EGYPT Your first mission takes you to Egypt Three giant stone pyramids were built there more than 3,000 years ago as burial tombs for Egyptian kings They still tower above the desert sands Your task is to figure out their sizes LEARN IT ABOUT NETS PYRAMIDS AND SURFACE AREAS A pyramid is a 3-D shape with a base and triangular faces A square-based pyramid has a square base and four triangular faces The top point of the pyramid is called its apex 04 apex face base A net is a flat pattern that is folded to make a 3-D shape The net of a square-based pyramid has four triangles the faces and a square the base joined together They can be joined in different ways One example is shown at right You can find the area of a rectangle by multiplying its length by its width So to find the area of a square multiply the length by itself To find the area of a triangle multiply the length of the base shown as b by the perpendicular height shown as h and divide the answer in half This can be shown as the formula area of a triangle ½b h To find the surface area of a pyramid find the area of each part of the net and add them together r a l u c i d n e p r e p h t h g i e h length of base b
GO FIGURE You need to find out the measurements of the pyramids so that you can add the information to your travel guide The tallest pyramid is called the Great Pyramid and was built for Pharaoh Khufu the second-tallest was built for Pharaoh Khafre and the shortest was built for Pharaoh Menkaure Plan of the site Side view with original heights and angles 143 5 m 146 5 m 230 4 m 65 5 m 215 2 m Khufu 51 3 53 2 51 8 Net of shapes 179 6 m m 906.9 Khafre 105 5m Menkaure 742 2 m the square base 1 For each pyramid find the area of 2 Due to erosion the height of Khufu’s pyramid the Great Pyramid has decreased since it was built It is now 7 7 m shorter What is its current height 186 3 m 05 84 4 m 3 Using the original heights shown above how much taller was the second-tallest pyramid than the shortest pyramid 4 For each of the pyramids use the nets to find the surface area of the whole 3-D shape
THE TAJ MAHAL Your next mission takes you to India to report on the Taj Mahal a beautiful burial structure that includes a reflecting pool Transformations are ways of moving geometric shapes They include reflection rotation and translation These three transformations do not change the size or angles of the shapes LEARN IT ABOUT TRANSFORMATIONS AND SYMMETRY MISSION 2 06 Reflections are made when shapes are flipped over a line showing what they would look like in a mirror Rotations are made when shapes are turned around a center point They can be turned by different amounts and in different directions Translations are made when you slide a shape without turning or reflecting it You can slide a shape horizontally vertically or diagonally The examples above show a quarter or 90 turn to the right
Symmetry is when a shape or object has parts that make it look the same when the shape is reflected or rotated Reflection symmetry is when one half of the shape is the reflection of the other half A line of symmetry is any folding line across the shape that makes the sides of the shape meet up exactly Rotational symmetry is when the shape looks the same after being turned The number of times it can be turned and look the same before it is upright again is called the order GO FIGURE For this section of the travel guide you need to describe the amazing patterns symmetries and geometric shapes found in the Taj Mahal Study the photos below that you took A B C a b c Shape Number of lines of reflection symmetry Order of rotational symmetry 0 1 5 1 1 5 D 07 does photo A show 1 How many lines of reflection symmetry 2 How many full translations are shown 3 Photo C shows a tile pattern made from in the repeating pattern in photo B three different shapes a equilateral triangles 3 equal sides b regular hexagons 6 sides 6 lines of symmetry and c another shape What is shape c 4 In total how many lines of symmetry do each of the shapes a b and c have 5 Photo D shows lawns shaped like the polygon drawn below Describe the shape by its number of sides as well as its number of lines of reflection and rotational symmetry How many right angles 90 does it have How many other kinds of angles
