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4 years ago

For the following question, find the surface area of the regular pyramid shown to the nearest whole number

Mathematics

1 answer:

devlian [24]4 years ago

7 0

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

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