Question

Part B if the height of each prism is 10 Cm what is the surface area prism

Answer 1

Prism A:

`Area = 288cm^2`

Prism B:

`Area =250cm^2`

Explanation:

Given

See attachment for prisms

`Height(h) = 10cm`

Required

Determine the surface area of both prisms

Prism A is triangular and as such, the surface area is:

`Area = 2 * A_b + (a + b + c) * h`

Where

`A_b = √(s * (s - a) * (s -b) * (s - c))`

and

`s = (a + b + c)/(2)`

Such that a, b and c are the lengths of the triangular sides of the prism.

From the attachment;

`a = 8; b =6; c =10`

So, we have:

`s = (a + b + c)/(2)`

`s = (8 + 6 + 10)/(2)`

`s = (24)/(2)`

`s = 12`

Also:

`A_b = √(s * (s - a) * (s -b) * (s - c))`

`A_b = √(12 * (12 - 8) * (12 - 6) * (12 - 10))`

`A_b = √(576)`

`A_b = 24`

So:

`Area = 2 * A_b + (a + b + c) * h`

`Area = 2 * 24 + (8 + 6 + 10) * 10`

`Area = 288cm^2`

Prism B is a rectangular prism. So, the area is calculated as:

`Area = 2 * (ab + bh + ah)`

From the attachment

`a = b = 5`

`h =10`

So:

`Area =2 * (5 * 5 + 5 * 10 + 5 * 10)`

`Area =250cm^2`