Answer:
2448 ft²
Step-by-step explanation:
The surface area of the triangular prism is the sum of the areas of the triangular bases and the lateral area of the rectangular faces.
Base area
The two right triangle bases together form a rectangle that is 24 ft wide and 18 ft tall. The total base area is ...
A = (24 ft)(18 ft) = 432 ft²
Lateral area
The rectangular faces of the prism are each 28 ft wide and have a total width of 18 +24 +30 = 72 ft. Their total area is ...
LA = (28 ft)(72 ft) = 2016 ft²
Total surface area
The sum of the base area and lateral area is ...
total area = (432 ft²) +(2016 ft²) = 2448 ft²
The surface area of the triangular prism is 2448 ft².
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Additional comment
The area formula for the triangular base is ...
A = 1/2bh . . . . . . area of one triangle with base b and height h
Then the area of the two congruent triangular bases is ...
A = 2(1/2bh) = bh
This is the formula we used above. It skips the work of dividing by 2, then multiplying by 2 again.
