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Geometry and Te Whare

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Geometry and Te Whare

A community group is planning a small square meeting space inspired by Te Whare Tapa Whā. Use geometry to check the design and explain how its pattern represents balance. Show working where needed.

The plan and its geometry

The floor plan is a square measuring 8 m by 8 m. The central gathering area is a square measuring 4 m by 4 m, centred inside it. The four equal surrounding regions represent the four dimensions of hauora: taha tinana (physical), taha hinengaro (mental and emotional), taha wairua (spiritual), and taha whānau (family and social).

1.The central gathering area is a square with side length 4 m. Calculate its area.

2.The whole room is 8 m by 8 m and the central area is 4 m by 4 m. Find the combined area of the four surrounding regions.

3.The 48 m² surrounding area is divided equally between the four dimensions of hauora. What is the area of each region?

4.Calculate the perimeter of the outer square room. Include the correct unit.

5.Which statement best describes the symmetry of a square plan with a centred square gathering area?

It has rotational symmetry of order 4 and four lines of symmetry.
It has rotational symmetry of order 2 and one line of symmetry.
It has no rotational symmetry and two lines of symmetry.
It has rotational symmetry of order 4 and no lines of symmetry.

6.A pattern on one surrounding region is turned a quarter-turn clockwise about the centre of the room to make the matching pattern in the next region. Name the transformation and state its angle.

7.Each corner of the square gathering area is a right angle. What is the size of one interior angle, and what is the sum of the four interior angles?

8.On a scale drawing, 1 cm represents 2 m. How long should each side of the 8 m by 8 m room be on the drawing? How long should each side of the 4 m by 4 m gathering area be?

9.A designer says, “Because the four surrounding regions have equal areas, they must all have the same shape.” Is this claim always true? Explain briefly.

10.In two or three sentences, explain how using symmetry and equal areas in this meeting-space plan could communicate balance among the four dimensions of Te Whare Tapa Whā. Use at least one geometry term.