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The area of a triangle is calculated using the formula A = 1/2 * b * h, where A is the area, b is the base length, and h is the height. To solve for the height, isolate h in the formula by getting rid of everything else on the right-hand side of the equation. Visualize b as the length of the base and h as the height of the triangle. This involves rearranging the formula to have h on one side of the equation.