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WINSTONCH [101]
2 years ago
14

A box is in the shape of an equilateral triangular prism. if the box is to be covered with paper on its lateral sides, how many

square inches of paper are needed?
Mathematics
1 answer:
Zarrin [17]2 years ago
7 0

The total surface area of the triangular prism that has a height of h and the side length of a is given below.

\rm a(\dfrac{\sqrt3}{2} \ a + 3h)

<h3>What is a triangular prism?</h3>

A triangular prism is a closed solid that has two parallel triangular bases connected by a rectangle surface.

A box is in the shape of an equilateral triangular prism.

If the box is to be covered with paper on its lateral sides.

Let a be the side length of the equilateral triangle and h be the height of the prism.

Then the surface area of the triangular prism will be

Surface area = 2 × area of triangle + 3 × area of the rectangle

The area of the triangle will be

\rm Area\ of\ triangle = \dfrac{\sqrt{3}a^2}{4}

The area of the rectangle will be

\rm Area \ of \ rectangle = a \ h

Then the total surface area will be

\rm Surface\ area =  2 \times \dfrac{\sqrt3 a^2 }{4} + 3 ah\\\\\\Surface\ area =  a(\dfrac{\sqrt3}{2} \ a + 3h)

More about the triangular prism link is given below.

brainly.com/question/21308574

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This question is incomplete, the complete question is:

An equilateral triangle has an apothem measuring 2.16 cm and a perimeter of 22.45 cm. What is the area of the equilateral triangle, rounded to the nearest tenth?

<h3>What is a triangle?</h3>

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Hence, option D)24.2cm² is the correct answer.

Learn more about triangles here: brainly.com/question/19305981

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