Given:
The right triangular prism.
Height of prism = 28 in.
Hypotenuse of base = 25 in.
leg of base = 24 in.
To find:
The lateral surface area of the prism.
Solution:
Pythagoras theorem:
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
Using Pythagoras theorem in the base triangle, we get
[tex]25^2=24^2+Base^2[/tex]
[tex]625-576=Base^2[/tex]
[tex]\sqrt{49}=Base[/tex]
[tex]7=Base[/tex]
The perimeter of the triangular base is:
[tex]P=7+25+24[/tex]
[tex]P=56[/tex]
Lateral area of a triangular prism is:
[tex]A=Ph[/tex]
Where, P is the perimeter of the triangular base and h is the height of the prism.
Putting [tex]P=56,h=28[/tex] in the above formula, we get
[tex]A=56(28)[/tex]
[tex]A=1568[/tex]
Therefore, the lateral area of the prism is 1568 in².
