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A right prism has height 7½ and triangular bases with sides of length 5, 12, and 13 What is the: Total Surface Area of the Prism

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.