Answer:
The answer is the first answer
P = 8 + 4√13 cm
A = 36 cm²
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