Question

Please help!!!!!!!!!!

Answer 1

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

$S=\sqrt{s(s-a)(s-b(s-c)}$,

where s is the semi-perimeter of the triangle; that is,

$s=\frac{a+b+c}{2}$.

So the permimeter of the triangle is

2p=4+5+3 = 12m

p = 6m

$S = \sqrt{p*(p-a)*(p-b)*(p-c)} = \sqrt{6*(6-3)*(6-4)*(6-5)} = \sqrt{6*3*2*1} =\sqrt{36} =6[m^{2} ]$

So the surface of the prism is a total sum of all surfaces:

P = 18m²+30m²+ 24m²+2*6m² = 84m²