A kite is designed on a rectangular grid with squares that measure 1cm by 1 cm. A hexagonal piece within the kite will be reserved for the company logo. Use the grid to identify the perimeter and area of the space reserved for the logo.

Answer:The answer is the first answerP = 8 + 8√17 cmA = 96 cm²Step-by-step explanation:* Lets study the figure - Its a kite with two diagonals- The shortest one is 12 cm- The longest one is 26 ⇒ axis of symmetry of the kite* To find the area reserved for the logo divide  the hexagonal piece into two congruent trapezium- The length of the two parallel bases are 4 cm and 8 cm and   its height is 8 cm- The length of non-parallel bases can calculated by Pythagoras rule∵ The lengths of the two perpendicular sides are 2 cm and 8 cm- 8 cm is the height of the trapezium- 2 cm its the difference between the 2 parallel bases ÷ 2   (8 - 4)/2 = 4/2 = 2 cm∴The length of the non-parallel base = √(2² + 8²) = 2√17* Now we can find the area of the space reserved for the logo- The area of the trapezium = (1/2)(b1 + b2) × h∴ The area = (1/2)(4 + 8) × 8 = (1/2)(12)(8) = 48 cm²∵ The space reserved for the logo are 2 trapezium∴ The area reserved for the logo = 2 × 48 = 96 cm²* The area of the reserved space for the logo = 96 cm²* The perimeter of the reserved space for the logo is the   perimeter of the hexagon∵ The lengths of the sides of the hexagon are:    4 cm , 4 cm , 2√17 cm , 2√17 cm , 2√17 cm , 2√17 cm∴ The perimeter = 2(4) + 4(2√17) = 8 + 8√17 cm* The perimeter of the reserved space for the logo = 8 + 8√17 cm