This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions for the given geometry problem: 1.1 Determine the area of the following: 1.1.1 ABJH ABJH is a square with side length x. Step 1: Identify the shape and its dimensions. ABJH is a square with side s = x units. Step 2: Apply the area formula for a square. Area = s^2 = x × x = x^2 units^2. x^2 units^2 1.1.2 BCDJ BCDJ is a rectangle. Step 1: Identify the shape and its dimensions. BCDJ is a rectangle with length BC = 6 units and width BJ = x units (since ABJH is a square, BJ = AB = x). Step 2: Apply the area formula for a rectangle. Area = length × width = BC × BJ = 6 × x = 6x units^2. 6x units^2 1.1.3 DEFJ DEFJ is a rectangle. Step 1: Identify the shape and its dimensions. DEFJ is a rectangle. From the diagram, JD = BC = 6 units. The total height CE = AG = AH + HG = x + 4 units. Also, CE = CD + DE. Since CD = BJ = x units, we have x + 4 = x + DE, which means DE = 4 units. Step 2: Apply the area formula for a rectangle. Area = length × width = JD × DE = 6 × 4 = 24 units^2. 24 units^2 1.1.4 HJFG HJFG is a rectangle. Step 1: Identify the shape and its dimensions. HJFG is a rectangle with length JH = x units (since ABJH is a square, JH = AH = x) and width HG = 4 units. Step 2: Apply the area formula for a rectangle. Area = length × width = JH × HG = x × 4 = 4x units^2. 4x units^2 1.2 Write in terms of x, the length of: 1.2.1 AC Step 1: Identify the segments that make up AC. The length AC is the sum of segments AB and BC. Step 2: Substitute the given lengths. AC = AB + BC = x + 6 units. (x + 6) units 1.2.2 AG Step 1: Identify the segments that make up AG. The length AG is the sum of segments AH and HG. Step 2: Substitute the given lengths. AG = AH + HG = x + 4 units. (x + 4) units Drop the next question! 📸