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3 years ago

What is the surface area of the triangular prism shown?

Mathematics

1 answer:

Degger [83]3 years ago

5 0

9514 1404 393

Answer:

(b) 976 m³

Step-by-step explanation:

The total surface area is the sum of the areas of the faces and bases.

The two bases are triangles, each with area ...

A = 1/2bh

So, the two of them together will have an area of ...

A = 2(1/2)bh = bh

where b is the base of the triangle, and h is its height. These values are shown as 14 m and 24 m, respectively.

Total base areas = (14 m)(24 m) = 336 m²

The total area of the rectangular faces is the sum of products of length and width. The width of each face is the same as the height of the prism, and the sum of face lengths is the perimeter of the triangular base.

The prism height is 10 m, and the perimeter of the base triangle is (14 m +25 m +25 m) = 64 m. Then the lateral area of the prism is ...

Total lateral area = (10 m)(64 m) = 640 m²

So, the total surface area of the prism is ...

base area + lateral area = 336 m² + 640 m² = 976 m²

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