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Pack A — Fluency

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Ecolint Campus des NationsMathematics
Year 7 · 7.7 Shape and Measure

Pack A · Fluency

Name: _________________________________
Date: _________________ Class: ___________

Answer all questions. Show your working. Questions are grouped by challenge level.

BronzeQuestions 1–10
  1. 1.
    A rectangle has perimeter 16 cm. Give two different pairs of whole-number side lengths that would produce this perimeter. Verify each pair by adding.
     
  2. 2.
    A triangle has sides 5 cm, 7 cm and 9 cm. What is its perimeter? Show the addition.
     
  3. 3.
    A rectangle has area 24 cm² with whole-number sides. Give three different (length, width) pairs. Verify each by multiplying.
     
  4. 4.
    Find the area of a rectangle with length 9 cm and width 4 cm. Show the multiplication and write the units.
     
  5. 5.
    A right-angled triangle has base 6 cm and height 8 cm. Find its area. Explain why you halve the rectangle formula.
     
  6. 6.
    A shape has 4 sides and 2 lines of symmetry. Name two possibilities and justify each.
     
  7. 7.
    A cuboid has length 4 cm, width 3 cm and height 2 cm. Find its volume by multiplying length × width × height. Show each step.
     
  8. 8.
    A regular polygon has perimeter 35 cm and each side is 7 cm. Find the number of sides by dividing. State the name of the polygon.
     
  9. 9.
    A rectangle has perimeter 26 cm and length 8 cm. Find the width by calculation. Then find the area.
     
  10. 10.
    A compound shape is made from two rectangles. Rectangle A is 6 cm × 4 cm. Rectangle B is 3 cm × 2 cm. Find the total area by calculating each area separately then adding.
     
SilverQuestions 11–20
  1. 11.
    Find the area of a parallelogram with base 9 cm and perpendicular height 5 cm.
     
  2. 12.
    Find the area of a trapezium with parallel sides 5 cm and 9 cm and perpendicular height 4 cm.
     
  3. 13.
    Find the volume of a cuboid with length 5 cm, width 4 cm and height 3 cm.
     
  4. 14.
    Find the surface area of a cuboid with length 5 cm, width 3 cm and height 2 cm.
     
  5. 15.
    A compound shape is made from a rectangle 8 cm by 6 cm with a 2 cm square removed from one corner. Find the area.
     
  6. 16.
    Find the perimeter of a regular 8-sided polygon with side length 5 cm.
     
  7. 17.
    A net is folded to make a cuboid with dimensions 4 cm × 3 cm × 2 cm. How many faces does it have and what is its surface area?
     
  8. 18.
    A triangle has base 8 cm and area 28 cm². Find its perpendicular height.
     
  9. 19.
    How many faces, edges and vertices does a triangular prism have?
     
  10. 20.
    A rectangle has a perimeter of 30 cm and a length of 9 cm. Find its width and hence its area.
     
GoldQuestions 21–30
  1. 21.
    A rectangle has area 24 cm² and width 3 cm. Find its perimeter.
     
  2. 22.
    A square has side 1.5 cm. Find its area in cm² and then convert it to mm².
     
  3. 23.
    A trapezium has parallel sides 4 cm and 8 cm. Its area is 30 cm². Find its perpendicular height.
     
  4. 24.
    A compound L-shape is formed by a large rectangle 10 cm by 8 cm with a smaller rectangle 4 cm by 3 cm cut from one corner. Find the area of the L-shape.
     
  5. 25.
    A rectangle has length (x+3)(x + 3) cm and width (2x)(2x) cm. Write an expression for its perimeter and simplify.
     
  6. 26.
    A rectangular garden is 3.2 m long and 2.5 m wide. Find its area in m² and convert the answer to cm².
     
  7. 27.
    A square has area 49 cm². Find its perimeter.
     
  8. 28.
    Find the surface area of a cuboid with dimensions 7 cm × 4 cm × 3 cm.
     
  9. 29.
    A rectangle is 12 cm long and 5 cm wide. What is three-quarters of its area?
     
  10. 30.
    A triangular prism has a triangular cross-section with base 6 cm and height 4 cm, and a length of 10 cm. Find its volume.
     
PlatinumQuestions 31–40
  1. 31.
    A rectangle has length (2x+1)(2x + 1) cm and width (x−2)(x - 2) cm. Its perimeter is 34 cm. Find xx and hence find the area.
     
  2. 32.
    A compound shape is made by joining a rectangle 10 cm × 6 cm and a triangle with base 6 cm and height 4 cm along a shared edge of length 6 cm. Find the total area.
     
  3. 33.
    A cuboid fish tank is 1.2 m long, 0.5 m wide and 0.4 m deep. It is filled to three-quarters of its height. Find the volume of water in litres. (1 m³ = 1 000 litres.)
     
  4. 34.
    A square tile has perimeter 28 cm. Tiles are arranged in a 4 × 5 grid with no gaps. Find the total area of the tiled surface in cm² and convert to m².
     
  5. 35.
    Two identical trapeziums, each with parallel sides 5 cm and 11 cm and perpendicular height 6 cm, are placed together along their longer parallel side to form a parallelogram. Find the area of the parallelogram.
     
  6. 36.
    A rectangle has length 10 cm and width 8 cm. Both dimensions are increased by 20%. Find the new area and the percentage increase in area.
     
  7. 37.
    A cuboid has volume 120 cm³. Its length is 6 cm and its width is 4 cm. Find its height and hence its surface area.
     
  8. 38.
    The area of a square is 196 cm². Express 196 as a product of prime factors, and hence write down the exact side length of the square.
     
  9. 39.
    A path of uniform width 2 cm runs around the outside of a rectangle 10 cm × 6 cm. Find the area of the path alone.
     
  10. 40.
    A cube has surface area 216 cm². Find its side length, volume and express the volume in litres.