KS3Solutions

Geometry and measures

Answers grouped by subtopic.

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Perimeter and area

  1. GM-Q1
    Answer
    Find the area of a rectangle 8 cm by 5 cm.
    Working
    1. Area = length × width = 8 × 5 = 40 cm2.
    Answer: 40 cm2
  2. GM-Q2
    Answer
    Find the perimeter of a rectangle 9 cm by 4 cm.
    Working
    1. Perimeter = 2 × (9 + 4) = 2 × 13 = 26 cm.
    Answer: 26 cm
  3. GM-Q3
    Answer
    Find the area of a triangle with base 10 cm and height 6 cm.
    Working
    1. Area = 0.5 × base × height = 0.5 × 10 × 6 = 30 cm2.
    Answer: 30 cm2

Volume

  1. GM-Q4
    Answer
    Find the volume of a cuboid 6 cm by 4 cm by 3 cm.
    Working
    1. Volume = length × width × height = 6 × 4 × 3 = 72 cm3.
    Answer: 72 cm3
  2. GM-Q5
    Answer
    A cylinder has radius 2 cm and height 5 cm. Find the volume. Use pi = 3.14.
    Working
    1. Area of base = π × r2 = 3.14 × 22 = 3.14 × 4 = 12.56 cm2.
    2. Volume = base area × height = 12.56 × 5 = 62.8 cm3.
    Answer: 62.8 cm3

Angles and properties

  1. GM-Q6
    Answer
    Two angles in a triangle are 45 degrees and 65 degrees. Find the third angle.
    Working
    1. Angles in a triangle sum to 180 degrees.
    2. Third angle = 180 - (45 + 65) = 180 - 110 = 70 degrees.
    Answer: 70 degrees
  2. GM-Q7
    Answer
    On a straight line, one angle is 110 degrees. Find the other angle.
    Working
    1. Angles on a straight line sum to 180 degrees.
    2. Other angle = 180 - 110 = 70 degrees.
    Answer: 70 degrees

Pythagoras

  1. GM-Q9
    Answer
    A right triangle has two shorter sides 6 cm and 8 cm. Find the hypotenuse.
    Working
    1. Use Pythagoras: c2 = 62 + 82 = 36 + 64 = 100.
    2. c = 10 cm.
    Answer: 10 cm
  2. GM-Q10
    Answer
    A right triangle has hypotenuse 13 cm and one side 5 cm. Find the remaining side.
    Working
    1. Use Pythagoras: other2 = 132 - 52 = 169 - 25 = 144.
    2. other = 12 cm.
    Answer: 12 cm

Transformations

  1. GM-Q11
    Answer
    Reflect the point (3, -2) in the 𝑥-axis. Give the new coordinates.
    Working
    1. Reflection in the 𝑥-axis keeps 𝑥 the same and changes the sign of 𝑦.
    Answer: (3, 2)
  2. GM-Q12
    Answer
    Rotate the point (2, 1) 90 degrees clockwise about the origin. Give the new coordinates.
    Working
    1. A 90 degree clockwise rotation uses (𝑥, 𝑦) -> (𝑦, -𝑥).
    2. So (2, 1) becomes (1, -2).
    Answer: (1, -2)
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