Question

Find the surface area of the figure. Round to the nearest tenths. DO NOT record units.

Answer 1

162.1

Explanation:

The surface area is just the areas of each of the sides of this prism. As the base of this triangular pyramid is an equilateral triangle, we know that the three lateral triangles are all congruent.

The area of an equilateral triangle is given by:
`A=(√(3) )/(4) s^2`, where s is the side length. Here, our base is an equilateral triangle with side length s = 8. Plug this in:

`A=(√(3) )/(4) s^2`

`A=(√(3) )/(4) *8^2=16√(3)` ≈ 27.7

The area of a regular triangle is:
`A=(1/2)bh`, where b is the base and h is the height. Here, b = 8 and h = 11.2. Plug this in:

`A=(1/2)bh`

`A=(1/2)*8*11.2=44.8`

Since there are three of this kind of triangle, we need to multiply 44.8 by 3:

44.8 * 3 = 134.4

Add this to the value above:

134.4 + 27.7 = 162.1

Hope this helps!