Which triangle has a larger area?
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Consider the yellow triangle:
s = 2 4 1 + 4 1 + 8 0 = 8 1
A y e l l o w = 8 1 ( 8 1 − 4 1 ) ( 8 1 − 4 1 ) ( 8 1 − 8 0 ) = 3 6 0
Consider the red triangle:
s = 2 4 1 + 4 1 + 1 8 = 5 0
A r e d = 5 0 ( 5 0 − 4 1 ) ( 5 0 − 4 1 ) ( 5 0 − 1 8 ) = 3 6 0
Hence, the areas are equal.
heron s formula as sides are equal areas are equal
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Area of Yellow triangle → 2 b a s e × h e i g h t = 2 8 0 × h e i g h t where height = 4 1 2 − 4 0 2 (By the Pythagorean theorem) → 9 ∴ Area of the yellow triangle → 2 8 0 × 9 = 3 6 0
Area of Red triangle → 2 b a s e × h e i g h t = 2 1 8 × h e i g h t where height = 4 1 2 − 9 2 (By the Pythagorean theorem) → 4 0 ∴ Area of the red triangle → 2 1 8 × 4 0 = 3 6 0
Hence, the 2 areas are EQUAL.