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Geometry in Design Basics

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Geometry in Design Basics

Ruben, Nikau and Tui are designing a new pizza box and shop logo. Use geometry to make their designs practical. Show working for calculations and include units where needed.

Read the design notes

The team is planning a square pizza box with sides of 32 cm. Its logo will be a circle with radius 5 cm. Inside the logo, two straight lines meet at the centre to make four sectors. For a hanging sign, they plan a triangular frame with interior angles of 48° and 67°.

1.A logo outline has five straight sides and five vertices. What is the name of this polygon?
2.Which statement must be true of a square pizza box lid?
  • It has four equal sides and four right angles.
  • It has exactly one pair of parallel sides.
  • Its opposite sides have different lengths.
  • It has three vertices.
3.The square box has a side length of 32 cm. Calculate the distance around its outside edge.
4.Work out the area of the square box lid, which measures 32 cm by 32 cm. Give your answer in square centimetres.
5.The circular logo has a radius of 5 cm. What is its diameter?
6.The triangular hanging-sign frame has interior angles of 48° and 67°. Find the third interior angle. Show the angle-sum calculation.
7.Ruben says, “The diagonals of a square are equal in length and meet at right angles.” Is his statement true or false?
  • True
  • False
8.Match each three-dimensional shape with the description of a net that could fold to make it.
  • Cube
  • Triangular prism
  • Square-based pyramid
  • Two triangles and three rectangles
  • One square and four triangles
  • Six squares
9.Sketch a simple pizza-shop logo using at least three different geometric shapes. Label each shape and mark one pair of parallel sides on your design.
10.Nikau suggests adding triangular braces to a rectangular sign frame. Explain one way triangles can help make a frame more stable.

2 printable pages

  • Geometry in Design Basics, page 1 of 2: Read the design notes

    Page 1

  • Geometry in Design Basics, page 2 of 2: 6. The triangular hanging-sign frame has interior angles of 48° and 67°. Find the third…

    Page 2

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