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The triangular faces of the prism shown are equilateral triangles with a perimeter of 48 cm. Each of the other faces is a square. Find the surface area of the prism

The triangular faces of the prism shown are equilateral triangles with a perimeter-example-1
User Gnijuohz
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Answer:

990.4 cm²

Explanation:

You want the surface area of an equilateral triangular prism with all edge lengths 16 cm. The height of the triangle is given as 13.9 cm.

Area

The area of the prism is the sum of the areas of the two triangular bases and the three square faces. The area of one base triangle is ...

A = 1/2bh

A = 1/2(16 cm)(13.9 cm)

There are two of these, so their total area is ...

B = 2(1/2)(16 cm)(13.9 cm) = (16·13.9) cm²

The 3 square faces have a total lateral area of ...

LA = 3(s²) = 3(16 cm)² = (16·48) cm²

Total

The total of these areas is ...

(16·13.9) +(16·48) cm² = 16(13.9 +48) cm² = 990.4 cm²

The surface area of the prism is 990.4 cm².

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The triangular faces of the prism shown are equilateral triangles with a perimeter-example-1
User Lupguo
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