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Sagot :
Given:
A right prism has height 7½ and triangular bases with sides of length 5, 12, and 13.
To find:
The total surface area of the prism.
Solution:
We have,
Height of prism = 7½ = 7.5
Sides of triangular base are 5, 12, 13. These sides of Pythagorean triplets because
[tex]5^2+12^2=13^2[/tex]
[tex]25+144=169[/tex]
[tex]169=169[/tex]
So, the base of the prism is a right triangle.
Area of a triangle is
[tex]Area=\dfrac{1}{2}\times base \times height[/tex]
[tex]A_1=\dfrac{1}{2}\times 5\times 12[/tex]
[tex]A_1=30[/tex]
The area of the base is equal to the area of the top, i.e., [tex]A_2=30[/tex] sq units.
Perimeter of the base is
[tex]P=5+12+13[/tex]
[tex]P=30[/tex]
The curved surface area of the prism is
[tex]CSA=\text{Perimeter of the base}\times \text{Height of the prism}[/tex]
[tex]CSA=30\times 7.5[/tex]
[tex]CSA=225[/tex]
Now, the total area of the prism is
[tex]A=A_1+A_2+CSA[/tex]
[tex]A=30+30+225[/tex]
[tex]A=285[/tex]
Therefore, the total surface area of the triangular prism is 285 square units.
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