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vladimir2022 [97]
2 years ago
11

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

Mathematics
1 answer:
sdas [7]2 years ago
5 0

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

5^2+12^2=13^2

25+144=169

169=169

So, the base of the prism is a right triangle.

Area of a triangle is

Area=\dfrac{1}{2}\times base \times height

A_1=\dfrac{1}{2}\times 5\times 12

A_1=30

The area of the base is equal to the area of the top, i.e., A_2=30 sq units.

Perimeter of the base is

P=5+12+13

P=30

The curved surface area of the prism is

CSA=\text{Perimeter of the base}\times \text{Height of the prism}

CSA=30\times 7.5

CSA=225

Now, the total area of the prism is

A=A_1+A_2+CSA

A=30+30+225

A=285

Therefore, the total surface area of the triangular prism is 285 square units.

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