Question

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 1

Answer:

The answer is the first answer

P = 8 + 4√13 cm

A = 36 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

- the shortest diagonal divides the longest into two parts

- The smallest part is 8 cm and the largest one is 18 cm

* 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 3 cm

- The length of non-parallel bases can calculated by Pythagoras rule

∵ The lengths of the two perpendicular sides are 2 cm and 3 cm

- 3 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 + 3²) = √13

* 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) × 3 = (1/2)(12)(3) = 18 cm²

∵ The space reserved for the logo are 2 trapezium

∴ The area reserved for the logo = 2 × 18 = 36 cm²

* The area of the reserved space for the logo = 36 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 , √13 cm , √13 cm , √13 cm , √13 cm

∴ The perimeter = 2(4) + 4(√13) = 8 + 4√13 cm

* The perimeter of the reserved space for the logo = 8 + 4√13 cm