Answer:
276 ft²
Step-by-step explanation:
The total surface area of a prism is the sum of its lateral area and the area of its bases. Here, the bases are two triangles, and the area of the sides is that of three rectangles.
base area
The area of a triangle is given by the formula ...
A = 1/2bh . . . . where b is the base of the triangle, h is its height
We have two identical triangles, so their total area will be ...
A = 2(1/2bh) = bh = (8 ft)(3 ft) = 24 ft²
lateral area
The sides of the prism are rectangles, all with the same length: 14 ft. Their total area will be that length multiplied by the total of the rectangle widths. That total is the same as the perimeter of the triangular base:
P = 5 ft + 5 ft + 8 ft = 18 ft
Then the lateral area is ...
lateral area = Ph = (18 ft)(14 ft) = 252 ft²
total area
The sum of the base area and lateral area is ...
(24 ft²) +(252 ft²) = 276 ft² . . . . area of the triangular prism
