0580/33 May/Jun 2023, Question 3: Interior and Exterior Angles of Polygons

Part (a) · 1 mark

Find the area of the shape drawn on the 1 cm² grid.

1. 1Bottom rectangle: 6 × 1 = 6 cm²
2. 2Two triangles on top: 2 × (1/2 × 2 × 1) = 2 cm²
3. 3Right-hand piece: half square + whole square = 0.5 + 1 = 1.5 cm²
4. 4Area = 6 + 2 + 1.5 = 9.5 cm²

Answer9.5

Part (b) · 1 mark

Calculate the perimeter of the 7 cm by 12 cm rectangle.

1. 1Perimeter = 7 + 12 + 7 + 12
2. 2= 38 cm

Answer38

Part (c) · 1 mark

Find the side length of a square whose area is 841 cm².

1. 1Side = √841
2. 2= 29 cm

Answer29

Part (di) · 1 mark

Find the volume of the cuboid built from 1 cm³ cubes.

1. 1The cuboid is 8 cubes long, 2 cubes deep and 3 cubes high
2. 2Volume = 8 × 2 × 3 = 48 cm³

Answer48

Part (dii) · 1 mark

State the dimensions of another cuboid using all the same cubes.

1. 1Any three whole numbers with product 48 other than 8, 2, 3
2. 2e.g. 4 × 4 × 3 = 48
3. 34 cm by 4 cm by 3 cm

AnswerCorrect dimensions

Part (e) · 3 marks

Find the shaded area between a radius 20 cm circle and three radius 4 cm circles, in terms of π.

1. 1Large circle area = π × 20² = 400π
2. 2Three small circles = 3 × π × 4² = 48π
3. 3Shaded area = 400π − 48π = 352π cm²

Answer352π

Part (fi) · 1 mark

Work out the interior angle of a regular 9-sided polygon with exterior angle 40°.

1. 1Interior angle = 180 − 40 = 140°

Answer140

Part (fii) · 4 marks

Find x, the angle between a regular pentagon side and a regular 9-sided polygon side at a shared vertex.

1. 1Pentagon exterior angle = 360 ÷ 5 = 72°, so interior angle = 180 − 72 = 108°
2. 2At the vertex: x + 108 + x = 140
3. 32x = 32
4. 4x = 16

Answer16

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