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Section 15.4 · Geometry and measure

Area of a triangle

Derive and use the formula for the area of a triangle, and use it in compound shapes.

6 teaching slides 55 practice questions Worked answers for every question

1 · Teaching slidesuse ← → keys

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2 · Key words

baseThe side you measure the height from.
perpendicular heightThe distance from the base to the opposite vertex, at right angles.
triangleA three-sided polygon.
parallelogramA quadrilateral with two pairs of parallel sides.
deriveWork a formula out, rather than being told it.

3 · Summary of the sectionrevise from this

  • Area of a triangle = ½ × base × perpendicular height.
  • It works because two copies of the triangle make a parallelogram of base × height.
  • The height must be perpendicular to the base — not a sloping side.
  • In an obtuse triangle the height falls outside the triangle. Extend the base and measure to it; the formula is unchanged.
  • Triangles with the same base and height have the same area, however different they look.
  • The answer may end in .5 — that is real, not a rounding error.
  • Area of a parallelogram = base × height, with no halving.
  • To find a missing base or height: double the area first, then divide.
  • Split a compound shape into rectangles and triangles and add.
PDFPrintable worksheet All 55 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons1 videos

Area of a Triangle

British corbettmaths

Half base times perpendicular height, including the obtuse case where the height falls outside.

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4 · Practice55 questions, easiest first

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15.3 Units of area
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15.5 Volume of cubes and cuboids