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What is the surface area?

What is the surface area?-example-1
User Greggory
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1 Answer

1 vote

Answer:

1856 ft²

Explanation:

You want the surface area of an isosceles triangular prism 23 ft long with a triangle base of 24 ft and a height of 16 ft.

Base area

The area of the two triangles is ...

A = 2 × 1/2bh = bh

A = (24 ft)(16 ft) = 384 ft²

Lateral area

The area of the three rectangular sides is ...

A = LW

A = (24 ft + 20 ft + 20 ft)(23 ft) = 64·23 ft² = 1472 ft²

Surface area

The surface area of the prism is the sum of the base area and the lateral area:

A = 384 ft² +1472 ft² = 1856 ft²

The surface area of the prism is 1856 square feet.

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Additional comment

We recognize each of the smaller right triangles that make up one base is a 3-4-5 right triangle with a scale factor of 4 ft. That makes the hypotenuse exactly 20 ft, as shown in the diagram.

The lateral area is effectively the product of the prism length (23 ft) and the perimeter of the triangular base.

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User Benjarwar
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8.4k points