Answer:
Prism A:
[tex]Area = 288cm^2[/tex]
Prism B:
[tex]Area =250cm^2[/tex]
Step-by-step explanation:
Given
See attachment for prisms
[tex]Height(h) = 10cm[/tex]
Required
Determine the surface area of both prisms
Prism A is triangular and as such, the surface area is:
[tex]Area = 2 * A_b + (a + b + c) * h[/tex]
Where
[tex]A_b = \sqrt{s * (s - a) * (s -b) * (s - c)}[/tex]
and
[tex]s = \frac{a + b + c}{2}[/tex]
Such that a, b and c are the lengths of the triangular sides of the prism.
From the attachment;
[tex]a = 8; b =6; c =10[/tex]
So, we have:
[tex]s = \frac{a + b + c}{2}[/tex]
[tex]s = \frac{8 + 6 + 10}{2}[/tex]
[tex]s = \frac{24}{2}[/tex]
[tex]s = 12[/tex]
Also:
[tex]A_b = \sqrt{s * (s - a) * (s -b) * (s - c)}[/tex]
[tex]A_b = \sqrt{12 * (12 - 8) * (12 - 6) * (12 - 10)}[/tex]
[tex]A_b = \sqrt{576}[/tex]
[tex]A_b = 24[/tex]
So:
[tex]Area = 2 * A_b + (a + b + c) * h[/tex]
[tex]Area = 2 * 24 + (8 + 6 + 10) * 10[/tex]
[tex]Area = 288cm^2[/tex]
Prism B is a rectangular prism. So, the area is calculated as:
[tex]Area = 2 * (ab + bh + ah)[/tex]
From the attachment
[tex]a = b = 5[/tex]
[tex]h =10[/tex]
So:
[tex]Area =2 * (5 * 5 + 5 * 10 + 5 * 10)[/tex]
[tex]Area =250cm^2[/tex]
