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Because the area is equal to half the base times height.

Suppose you start of with a triangle with base = B cm and height = H cm.

Its area = 1/2*B*H cm2.

You then double the base to 2B cm and halve the height to H/2 cm and tis gives the new area = 1/2*(2B)*(H/2) = 1/2*B*H cm2, as before.

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