Answer:
300 square units
Explanation:
You want the total surface area of the triangular prism shown.
Base area
There are two triangular bases, each of which is a right triangle with legs of length 5 and 12. The area of each triangle is half the product of these leg lengths, so the two triangles together have an area that is ...
total base area = bh = (12)(5) = 60 . . . . square units
Lateral area
The lateral area of the prism is the sum of the areas of the rectangles. Each has a width of 8 units, so we can add lengths to compute the total area.
LA = Ph . . . . . where P is the perimeter of the base, h is the prism height
LA = (5 +12 +13)(8) = 30(8) = 240 . . . . square units
Total area
The total surface area of the prism is the sum of the base area and the lateral area:
surface area = 60 +240 = 300 . . . . square units
The surface area of the prism is 300 square units.
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