Answer:
[tex]SA=504\text{ cm}^2[/tex]
Step-by-step explanation:
We have been given an a right angled triangular prism. We are asked to find the surface area of our given prism.
We will use surface area of right prism formula to solve our given problem.
[tex]SA=2B+Ph[/tex], where,
SA = Surface area,
B = Area of right triangular base,
P = Perimeter of right triangular base,
h = Height of prism.
Let us find area of of triangular base.
[tex]B=\frac{1}{2}\times 9\times 12[/tex]
[tex]B=9\times 6[/tex]
[tex]B=54[/tex]
The perimeter of triangular base would be [tex]9+12+15=36[/tex].
Upon substituting our given values, we will get:
[tex]SA=2(54)+36(11)[/tex]
[tex]SA=108+396[/tex]
[tex]SA=504[/tex]
Therefore, the surface area of our given prism is 504 square cm.
Surface area of a solid object is the sum of the areas of all the faces. The surface area of the right angled triangular prism is 504 squared cm.
Surface area of a solid object is the sum of the areas of all the faces.
Surface area of the right angled triangular prism can be given as,
[tex]A_s=Ph+2(A_b)[/tex]
Here, [tex]P[/tex] is the perimeter of the right triangular base, [tex]h[/tex] is the height of the prism and [tex]A_s[/tex] is the area of the base.
Given information-
Area of base is the half of the product of height and base of the right triangle triangle and the perimeter triangular base is the sum of all its sides.
Thus the surface area of the right angled triangular prism is,
[tex]A_s=Ph+2(A_b)\\A_S=(9+12+15)\times 11+2\times(\dfrac{1}{2} \times9\times12)\\A_s=36\times11+108\\A_s=396+108\\A_s=504[/tex]
Hence the surface area of the right angled triangular prism is 504 squared cm.
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