Answer:
The surface of the prism is 84m²
Step-by-step explanation:
You have 4 figures here (two the same triangles)
you need to determine the surface of each and then sum it to one. This will be your final surface.
rectangles:
3*6= 18m²
5*6 = 30m²
4*6 = 24m²
triangles:
You need to determine the square of the triangles from the Heron's formula.
Heron's formula states that the area of a triangle whose sides have lengths a, b, and c is
[tex]S=\sqrt{s(s-a)(s-b(s-c)}[/tex],
where s is the semi-perimeter of the triangle; that is,
[tex]s=\frac{a+b+c}{2}[/tex].
So the permimeter of the triangle is
2p=4+5+3 = 12m
p = 6m
[tex]S = \sqrt{p*(p-a)*(p-b)*(p-c)} = \sqrt{6*(6-3)*(6-4)*(6-5)} = \sqrt{6*3*2*1} =\sqrt{36} =6[m^{2} ][/tex]
So the surface of the prism is a total sum of all surfaces:
P = 18m²+30m²+ 24m²+2*6m² = 84m²
