Answer:
The surface area = 650 m² ⇒ the third answer
Step-by-step explanation:
* Lets describe the figure
- Its a regular pyramid withe hexagonal base
- It has 6 isosceles triangular faces
- All the sides of the hexagon are equal
* To find the surface area of the pyramid find the area of the 7 faces
- The hexagon formed from 6 equilateral triangles
∴ The area of the hexagon = 6 × 1/2 × base × height
∵ The length of the base = 10 ⇒ given
∵ The length of the height of each triangle = 5√√3 ⇒ given
∴ The area of the hexagon = 6 × 1/2 × 10 × 5√3 = 150√3 m²
* Now lets calculate the area of the side faces
∵ The side face is a triangle with base length 10 and height 13
∴ The area of the side faces = 6 × 1/2 × 10 × 13 = 390 m²
- The total surface are = 150√3 + 390 = 649.8076 ≅ 650 m²
