Answer:
[tex]A = 144\ cm^{2}[/tex]
Step-by-step explanation:
Let A be the surface area of the triangular prism
Given:
A triangular prism
Height [tex]h = 4\ cm[/tex]
Base [tex]b = 8\ cm[/tex]
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.
[tex]Surface\ Area = Lateral Area + 2(Base\ Area)[/tex]
[tex]A = A_{L} + 2(A_{B})[/tex] -------------(1)
First We calculate the lateral surface area of the triangular prism.
[tex]Lateral\ surface\ area = Perimeter\ of\ the\ base\ triangle\times Height[/tex]
[tex]Lateral\ surface\ area = Perimeter\ of\ the\ base\ triangle\times Height[/tex]
[tex]A_{L} = p\times h[/tex]
Perimeter of the base and height are known, so we substitute these value in above equation.
[tex]A_{L} = 24\times 4[/tex]
[tex]A_{L} = 96\ cm^{2}[/tex]
Therefore the lateral surface area of the triangular prism [tex]A_{L} = 96\ cm^{2}[/tex]
Now we calculate area of the base.
[tex]Area\ of\ base = \frac{1}{2}bh[/tex]
Where b = base and h = Height are known.
[tex]Area\ of\ base = \frac{1}{2}\times 8\times 6[/tex]
[tex]Area\ of\ base = 4\times 6[/tex]
[tex]Area\ of\ base = 24\ cm^{2}[/tex]
So the area of the base [tex]A_{B) = 24\ cm^{2}[/tex]
Substitute Lateral surface area and base area in equation 1.
[tex]A = 96 + 2(24)[/tex]
[tex]A = 96 + 48[/tex]
[tex]A = 144\ cm^{2}[/tex]
Therefore the surface area of the triangular prism [tex]A = 144\ cm^{2}[/tex]
