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Lesson 10 of 11

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9 min

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Eight ideas, eight checks. Read the table first.

Area — eight rules for flat space
IdeaHow it goes
Counting squaresWhole squares, plus what the part squares hold.
A rectangleLength × width, whole numbers or not.
A parallelogramBase × the height, measured square across.
A triangleHalf of base × the height.
The heightSquare across, from the base to the far corner.
A trapeziumAverage the two parallel sides, × the height.
Awkward outlinesSplit into simple shapes, then add or take away.
Square unitsUse the side change twice: 100 × 100.

A shape on centimetre paper fills 14 whole squares. It reaches into 9 more, holding 4.5. What is its area?

  • 14 cm², because only whole squares count
  • 18.5 cm²
  • 23 cm², because it touches 23 squares

A verandah is 7 m long and 3.5 m wide. What area does it cover?

  • 21 m², because the half row is dropped
  • 24.5 m²
  • 10.5 m², because 7 + 3.5 is 10.5

A parallelogram has a base of 12. Its parallel sides are 5 apart. Its slanted side is 7. What is its area?

  • 84, because 12 × 7 is 84
  • 60
  • 24, because 12 + 5 + 7 is 24

A triangle has a base of 14. Its far corner is 5 from the base line. What is its area?

  • 70, because base times height is 70
  • 35
  • 19, because 14 + 5 is 19

A triangle has a base of 6. Its other two sides are both 5. Its height is 4. What is its area?

  • 15, because half of 6 × 5 is 15
  • 12
  • 24, because 6 × 4 is 24

A trapezium has parallel sides of 9 and 15. They are 6 apart. What is its area?

  • 810, because 9 × 15 × 6 is 810
  • 72
  • 90, because the longer side times the height is 90

A four-sided shape has a diagonal of 10. The other corners are 3 and 4 from it, on opposite sides. What is its area?

  • 70, because 10 × 7 is 70
  • 35
  • 12, because 3 × 4 is 12

A floor is 3 square metres. How many square centimetres is that?

  • 300, because a metre is a hundred centimetres
  • 30,000
  • 3,000, because you add three zeros for metres

Your book calls this Part II, Chapter 7. Its name is Area. Use the height habit there.

Next: We Distribute, Yet Things Multiply.

Reveal every answer to finish this lesson.

That is the end of this subject for Class 8

Nicely done. There is more waiting at this same level — pick whichever you like.