2.5 Area of Polygons

• Area of triangles, parallelograms, rhombuses and trapeziums
• Area of regular polygons
• Area of composite and irregular shapes
• Applications of area in real life

• calculate the area of triangles and quadrilaterals
• calculate the area of regular polygons
• find the area of composite shapes by decomposition
• apply area calculations to real life situations

“How do you find the area of a shape that has no formula?”

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1. Areas of triangles and quadrilaterals
   40 min · 2 practice tasks · quiz
   The standard formulas, and where each one comes from.
2. Regular polygons and composite shapes
   40 min · 2 practice tasks · quiz
   Splitting any shape into parts you can already handle.
3. Perpendicular height, not the slant
   40 min · 1 practice tasks · quiz
   Area uses the straight-up height between parallel sides; if only a slant is given, find that height first.
4. Triangle area from two sides and the included angle
   40 min · 1 practice tasks · quiz
   When the perpendicular height is not given, area is half the product of two sides times the sine of the angle between them.
5. Heron's formula: three sides, no height
   40 min · 1 practice tasks · quiz
   When you know all three sides of a triangle and no angle or height, use the semi-perimeter in Heron's formula.
6. Area of a parallelogram from sides and an angle
   40 min · 1 practice tasks · quiz
   A parallelogram is two copies of the same triangle: area is base times height, or a b sin C.
7. Rhombus: base times height, or half the diagonals
   40 min · 1 practice tasks · quiz
   A rhombus is a parallelogram with equal sides, so both b h and half d1 d2 work; choose the data you have.
8. Area of a kite
   40 min · 1 practice tasks · quiz
   A kite has perpendicular diagonals, so its area is also half d1 times d2; only the symmetry diagonal is bisected.
9. Trapezium: finding a missing length
   40 min · 1 practice tasks · quiz
   Given the area of a trapezium and three of a, b, h, rearrange half (a + b) times h to find the missing one.
10. A regular polygon as n isosceles triangles
    40 min · 1 practice tasks · quiz
    From the centre, a regular n-gon is n identical isosceles triangles; area is half the perimeter times the apothem.
11. Frames, paths and holes: subtract to add
    40 min · 1 practice tasks · quiz
    A frame or a path around a lawn is the outer area minus the inner area; a T-shape or courtyard is the same idea.
12. Irregular polygons by triangulation
    40 min · 1 practice tasks · quiz
    Any polygon can be cut into triangles; add those areas. For a plot, measure enough sides and diagonals (or use Heron).
13. Square metres, hectares and acres
    40 min · 1 practice tasks · quiz
    Kenyan land is quoted in hectares and acres; convert through square metres so the scale of 10 000 does not get lost.
14. Paint, tiles, fertiliser and land cost
    40 min · 1 practice tasks · quiz
    Area decides how much paint, how many tiles, how much fertiliser and how much a plot costs; always convert units and round materials up.