Question 1: The area of a regular hexagon knowing one of its sides by definition is given by: A = (3 * root (3) * L ^ 2) / (2) Substituting values we have: A = (3 * root (3) * (10) ^ 2) / (2) A = 259.8076211 Rounding off we have: A = 259.8 squeare feet Answer: the area of the floor is: A = 259.8 squeare feet option B
Question 2: We search the are of each sector separately: For Den: A1 = (16) * (16) A1 = 256 For Entrance: A2 = (4) * (4) A2 = 16 For Kitchen: A3 = (12) * (6) + (6) * (6) A3 = 72 + 36 A3 = 108 The total area is: A = A1 + A2 + A3 Substituting: A = 256 + 16 + 108 A = 380 square feet Answer: A = 380 square feet option F
Question 3: For this case we look for the area of the two shaded triangles. We have then: Triangle 1: A1 = (1/2) * (3) * (4) A1 = 6 Triangle 2: A2 = (1/2) * (3) * (4 + 5) A2 = 13.5 The area of the shaded region is the sum of the areas: A = A1 + A2 Substituting: A = 6 + 13.5 A = 19.5 square units Answer: A = 19.5 square units option D
Question 4: The area of the parallelogram by definition is: A = (b) * (h) Where, b: base h: height Substituting values we have: A = (15) * (15 + 6) A = 315 square centimeters Answer: A = 315 square centimeters option J