Question

Please can someone help me work out the surface area​

Answer 1

`A = 144\ cm^(2)`

Explanation:

Let A be the surface area of the triangular prism

Given:

A triangular prism

Height
`h = 4\ cm`

Base
`b = 8\ cm`

Perimeter of the base triangle (p = 6 + 8 + 10 = 24 cm)

Now we calculate the surface area of the triangular prism.

Solution:

We know that the surface area of the triangular prism.

`Surface\ Area = Lateral Area + 2(Base\ Area)`

`A = A_(L) + 2(A_(B))` -------------(1)

First We calculate the lateral surface area of the triangular prism.

`Lateral\ surface\ area = Perimeter\ of\ the\ base\ triangle* Height`

`Lateral\ surface\ area = Perimeter\ of\ the\ base\ triangle* Height`

`A_(L) = p* h`

Perimeter of the base and height are known, so we substitute these value in above equation.

`A_(L) = 24* 4`

`A_(L) = 96\ cm^(2)`

Therefore the lateral surface area of the triangular prism
`A_(L) = 96\ cm^(2)`

Now we calculate area of the base.

`Area\ of\ base = (1)/(2)bh`

Where b = base and h = Height are known.

`Area\ of\ base = (1)/(2)* 8* 6`

`Area\ of\ base = 4* 6`

`Area\ of\ base = 24\ cm^(2)`

So the area of the base
`A_{B) = 24\ cm^(2)`

Substitute Lateral surface area and base area in equation 1.

`A = 96 + 2(24)`

`A = 96 + 48`

`A = 144\ cm^(2)`

Therefore the surface area of the triangular prism
`A = 144\ cm^(2)`