Question

What is the correct answer

Answer 1

248
`mm^(2)`

Explanation:

Instead of calculating for the hexagon, divide it into 5 separate triangles with a 8mm base and 5.5mm height. Calculate using the "half base times height" formula and multiply it by five for the hexagon's area:

`(1)/(2)((b)(h)) (5)\\(1)/(2)((8)(5.5)) (5)\\\\ (1)/(2)(44) (5)\\\\(22)(5)\\110`

This is the area of the pentagonal pyramid's base. Now for the sides calculate the area of an individual side (triangle with base 8mm and height 6.9mm) then multiply by 5 for the area of all the sides:

`(1)/(2)((b)(h)) (5)\\\\(1)/(2)((8)(6.9)) (5)\\\\(1)/(2)(55.2) (5)\\\\(27.6) (5)\\\\138\\`

For the total surface area of this shape add these values together for 110+138=248mm
`mm^(2)`

I hope that this helps :)