1. **Problem Statement:** You are given rectangle ADCB with area 108 cm², side BA = 6 cm, and DC = ED. You need to find: - Length of rectangle ADCB (side AD) - Area of triangle ADC - Area of shaded triangle AEC 2. **Step 1: Find length AD of rectangle ADCB** - Recall the area formula for a rectangle: $$\text{Area} = \text{length} \times \text{width}$$ - Here, width BA = 6 cm, area = 108 cm² - Use formula: $$108 = AD \times 6$$ - Solve for AD by dividing both sides by 6: $$AD = \frac{108}{6}$$ - Simplify the fraction by canceling common factors: $$AD = \frac{\cancel{108}}{\cancel{6}} = 18$$ 3. **Step 2: Find area of triangle ADC** - Triangle ADC is formed by diagonal AC of rectangle ADCB - Area of triangle = half the area of rectangle because diagonal divides rectangle into two equal triangles - Use formula: $$\text{Area of } \triangle ADC = \frac{1}{2} \times \text{Area of rectangle}$$ - Substitute values: $$= \frac{1}{2} \times 108$$ - Simplify: $$= 54$$ 4. **Step 3: Find area of shaded triangle AEC** - Point E lies on AD such that DC = ED - Use properties of rectangle and triangle area formulas - Express length ED in terms of AD and use it to find length AE - Use formula for area of triangle: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ - Identify base and height for triangle AEC - Calculate area using lengths found This step-by-step approach will help you solve each part without directly giving the final answers. Try applying these steps carefully.