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.
<h3>Base area</h3>
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
<h3>Lateral area</h3>
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
<h3>Total surface area</h3>
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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<em>Additional comment</em>
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.
