Akite 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.

The answer is the first answer

P = 8 + 8√17 cm

A = 96 cm²

Step-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