Chapter 14: Maps and Locations

On a town grid map, columns are numbered 1 to 6 (West to East) and rows are lettered A to F (South to North).
• Town Hall is at (2, B)
• Railway Station is at (5, B)
• Public Hospital is at (2, E)
(a) In which compass direction is the Hospital from the Town Hall?
(b) In which compass direction is the Railway Station from the Town Hall?
(c) If 1 grid square represents 200 m, find the straight-line ground distance between Town Hall and Railway Station.

Explain the difference between a 'Floor Map' (2D layout) and a 'Deep Drawing' (3D perspective sketch) of a house. Why can't windows on the back wall be seen in a front deep drawing?

A student builds a block structure using 5 unit cubes: 3 cubes placed in a row on the table, and 2 cubes stacked on top of the first and second cubes.
(a) Describe the Front View.
(b) Describe the Side View.
(c) Describe the Top View.

A cube has 6 square faces.
(a) Draw or describe two different valid 6-square nets that can be folded to form a cube.
(b) Can 6 squares arranged in a single straight row (1 × 6) fold into a cube? Explain why.

On a school campus grid map, an athlete runs from Pavilion (1, 1) to Flagpost (4, 5).
(a) How many units East and how many units North must he run?
(b) If each grid square is 40 m × 40 m, find the total distance run along the grid lines.

An open box without a top lid has 5 square faces.
(a) Describe the plus-sign (+) shaped net of an open box.
(b) If each square face of the net has side 6 cm, find the total surface area of the open box.

On a standard playing die, the numbers on opposite faces always add up to 7.
(a) What number is on the face opposite to 2?
(b) What number is opposite to 4?
(c) What number is opposite to 6?

What is isometric dot paper used for in mathematics? How do the triangular grids of isometric dots help in drawing 3D cubes accurately?

Students build a bridge model using matchboxes: 2 pillars on either side (each 3 matchboxes high) and a horizontal deck of 4 matchboxes across the top.
(a) What will the front view look like?
(b) What will the top view look like?

On an architectural floor map, doors and windows have standardized representations.
(a) How is a door typically represented?
(b) How is a window represented on a wall?

A square sheet of metal measuring 20 cm × 20 cm has four 4 cm × 4 cm squares cut out from its four corners. The four flaps are then folded upward to make an open rectangular tray.
(a) What is the length and width of the base of the tray?
(b) What is the height of the tray?
(c) Find the volume of the tray in cubic centimetres ($V = L \times W \times H$).

Follow the route instructions: Start at Depot (0, 0). Walk 3 units East, 4 units North, 2 units West, and 1 unit South.
(a) What are the coordinates of the destination?
(b) In which compass quadrant from the Depot is the destination?

(a) What 2D shapes make up the net of a closed cylinder?
(b) What 2D shapes make up the net of a cone?

A solid rectangular block is built using unit cubes: it is 4 cubes long, 3 cubes wide, and 2 cubes high.
(a) How many unit cubes are used in total?
(b) How many cubes are on the bottom layer?
(c) If all outside faces are painted red, how many cubes have paint on exactly 3 faces (corner cubes)?

A sports ground on a town map occupies grid blocks from Column 2 to 5 and Row C to F.
(a) How many grid units long and wide is the ground?
(b) How many square grid blocks does it cover?
(c) If 1 block is 100 m × 100 m, find its actual area in square metres.

Why do architects draw both a 2D floor blueprint and a 3D isometric perspective drawing before constructing a building?

State the number of Faces ($F$), Edges ($E$), and Vertices ($V$) for:
(a) A triangular prism
(b) A square pyramid
Verify Euler's formula: $F - E + V = 2$ for both.

A survey drone flies overhead taking continuous vertical photographs.
(a) How are the drone photos stitched together to create a digital cadastral map?
(b) What mathematical scale factor links pixels on screen to ground metres?

A cube has letters A, B, C, D, E, F on its 6 faces. When unfolded into a T-shaped net, A is on the top square, B is in the center, C is below B, D is to the left of B, E is to the right of B, and F is at the bottom. Which face is opposite to Face B?

A door on a floor plan has width 90 cm and swings through a 90° arc.
(a) What shape of floor space must be kept completely clear of furniture?
(b) Find the area of this clearance quadrant in square metres (take $\pi \approx 3.14$, $A = \frac{1}{4} \pi r^2$).

On a standard Cartesian coordinate grid with origin (0, 0) at center:
(a) Positive X-axis points in which compass direction?
(b) Positive Y-axis points in which compass direction?
(c) Point (-3, -3) lies in which compass direction from the origin?

At 8:00 AM, a vertical flagpole casts a long shadow on the ground.
(a) In which compass direction does the shadow point in the morning?
(b) In which direction does the shadow point at 4:00 PM in the evening?
(c) At what time of day is the shadow shortest?

State True or False with reasoning:
(a) A cylinder has 2 flat faces and 1 curved face.
(b) A 2D floor map shows how tall a house is.
(c) Isometric drawings make parallel lines appear to meet at a point.

A student draws a model map of his school ground with scale 1 cm = 20 m. The football field measures 5 cm by 3 cm on the map.
(a) Find the actual dimensions of the football field.
(b) What is its actual ground area in square metres?
(c) If an athlete runs 4 complete laps around the perimeter of the field, how many metres does he run?