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Lesson 4 of 11

Two of the same triangle, fitted together

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7 min

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Take a triangle and make an identical copy. Turn the copy half way round. Fit the two together. What shape do they make?

A triangle, base 10, height 6.
Step 1 of 4
  1. A triangle, base 10, height 6.
  2. A copy of it, turned round a point.
  3. Together they make a parallelogram.
  4. 10 × 6 = 60, so 30 each.

Two equal pieces, each half

The two triangles make a parallelogram, with nothing left over. The copy is the triangle turned half way round. So the triangle is half of the parallelogram. The parallelogram has the same base and height as the triangle.

Rule: area of a triangle = ½ × base × height.

Take base 10 and height 6. The parallelogram is 10 × 6 = 60. The triangle is half of that: 60 ÷ 2 = 30. This works for any triangle, even a leaning one.

Turn the copy. Find the turn that fits.

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