Respuesta :
Given:
The bases of triangular prism are right triangles with a base of 12 inches and height of 9 inches.
The height of the prism is 11 inches.
To find:
The surface area of the triangular prism.
Solution:
Using the Pythagoras theorem, the hypotenuse of the bases of the triangular prism is:
[tex]Hypotenuse^2=Base^2+Height^2[/tex]
[tex]Hypotenuse^2=12^2+9^2[/tex]
[tex]Hypotenuse^2=144+81[/tex]
[tex]Hypotenuse^2=225[/tex]
Taking square root on both sides.
[tex]Hypotenuse=15[/tex]
The surface after of the triangular prism contains 3 rectangles of dimensions 12 inches by 11 inches, 9 inches by 11 inches, 15 inches by 11 inches and two triangles with base 12 inches and height 9 inches.
Area of the rectangle:
[tex]Area=Length \times Width[/tex]
So, the area of three rectangles are:
[tex]A_1=12 \times 11[/tex]
[tex]A_1=132[/tex]
[tex]A_2=9 \times 11[/tex]
[tex]A_2=99[/tex]
[tex]A_3=15 \times 11[/tex]
[tex]A_3=165[/tex]
Area of a triangle is:
[tex]Area=\dfrac{1}{2}\times base \times height[/tex]
So, the area of the triangles is:
[tex]A_4=\dfrac{1}{2}\times 12 \times 9[/tex]
[tex]A_4=6 \times 9[/tex]
[tex]A_4=54[/tex]
And, the triangles have same dimensions so their areas are equal.
[tex]A_4=A_5=54[/tex]
Now,
[tex]Area=A_1+A_2+A_3+A_4+A_5[/tex]
[tex]Area=132+99+165+54+54[/tex]
[tex]Area=504[/tex]
Therefore, the surface area of the triangular prism is 504 sq. inches.
