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Summary of important concepts

Area of Triangles and Parallelograms

Solve problems involving the area of triangles and parallelograms using established formulas and appropriate units.

Both formulas come from the rectangle. A parallelogram is a rectangle pushed over; a triangle is half of one.

Method

Parallelogram
A=bhA = bh
Base times perpendicular height.
Triangle
A=12bhA = \tfrac{1}{2}bh
Exactly half the parallelogram on the same base.
Height means perpendicular height
The straight-up distance, not the slanted side. This is the usual error.

Worked example

e.g. Find the area of a triangle with base 10 cm and height 6 cm.\text{Find the area of a triangle with base } 10\text{ cm and height } 6\text{ cm.}
  1. Write the formula before substituting anything.A=12bhA = \tfrac{1}{2}bh
  2. Identify the base and the perpendicular height.b=10h=6b = 10 \quad h = 6
  3. Substitute.A=12×10×6A = \tfrac{1}{2} \times 10 \times 6
  4. Work it out.A=30A = 30
  5. Write the answer with square units.A=30 cm2A = 30\text{ cm}^2

Practice

Write the formula first. Watch for the perpendicular height.

1
Parallelogram, b=8, h=5\text{Parallelogram, } b=8,\ h=5
Answer40 cm240\text{ cm}^2
2
Triangle, b=12, h=7\text{Triangle, } b=12,\ h=7
Answer42 cm242\text{ cm}^2
3
Triangle with area 24 and base 8. Find h.\text{Triangle with area } 24 \text{ and base } 8. \text{ Find } h.
Answerh=6h = 6
4
A triangle has slant side 13 and height 12. Which do you use?\text{A triangle has slant side } 13 \text{ and height } 12. \text{ Which do you use?}
Answerthe height, 12\text{the height, } 12
5
Why is a triangle half a parallelogram?\text{Why is a triangle half a parallelogram?}
AnswerTwo identical triangles join to make one.\text{Two identical triangles join to make one.}
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