Question

Solve problems and show work for all of them

Answer 1

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