1. **Problem statement:** Determine the area of the shaded triangle AEC in the given figure. 2. **Given information:** - Rectangle ADCB has area 108 cm². - Side BA = 6 cm. - DC = ED. - We want the area of triangle AEC. 3. **Step 1: Find the length of AD (length of the rectangle).** Since ADCB is a rectangle, area = length × width. Given area = 108 cm² and width BA = 6 cm, $$\text{length} = \frac{\text{area}}{\text{width}} = \frac{108}{6} = 18 \text{ cm}.$$ So, AD = 18 cm. 4. **Step 2: Understand the position of point E.** Since DC = ED and DC is a side of the rectangle with length 18 cm, point E lies on the extension of DC such that ED = DC = 18 cm. 5. **Step 3: Coordinates for calculation (assuming A at origin):** - Let A = (0,0) - B = (0,6) - D = (18,0) - C = (18,6) - E lies on line extending from D to the right, so E = (18 + 18, 0) = (36,0) 6. **Step 4: Calculate area of triangle AEC with vertices A(0,0), E(36,0), C(18,6).** Use the formula for area of triangle with coordinates: $$\text{Area} = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$$ Substitute: $$= \frac{1}{2} |0(0 - 6) + 36(6 - 0) + 18(0 - 0)| = \frac{1}{2} |0 + 216 + 0| = \frac{216}{2} = 108 \text{ cm}^2.$$ 7. **Final answer:** The area of the shaded triangle AEC is **108 cm²**.