Foundation and Higher · area formulae
Three area formulae.
One idea behind
all of them.
stop memorising,
start seeing
it all comes back to a —
Rectangle
area = base × height
other shapes rearrange into one
area formula 1 of 3
Parallelogram
1. Cut the triangle off one end…
2. …slide it to the other. A rectangle.
✓ Area = base × perpendicular height
= 8 × 5 = 40 cm²
area formula 2 of 3
Triangle
1. Make a copy and turn it round.
2. Two triangles make a parallelogram,
so one triangle is half of it.
✓ Area = ½ × base × height
= ½ × 6 × 4 = 12 cm²
area formula 3 of 3
Trapezium
1. Same trick: copy it and turn it round.
2. A parallelogram with base a + b.
The trapezium is half of it.
✓ Area = ½ × (a + b) × height
= ½ × 12 × 5 = 30 cm²
three formulae, one idea —
Parallelogram
base × height
Triangle
half × base × height
Trapezium
half × (a + b) × height
Height means straight up —
never the slanted side.
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