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To find the area of a right-angled triangle with a 30° angle and perimeter of 30 units, first identify it as a 30-60-90 triangle with side ratios X, 2X, and X√3. Using the perimeter equation X + 2X + X√3 = 30, solve for X by rationalizing the denominator to get X = 5(3 - √3). Then apply the area formula 1/2 × base × height = 1/2 × X × X√3, which simplifies to 75(2√3 - 3) square units, approximately 34.81 square units.