Answer:
1192 ft²
Step-by-step explanation:
Figure 3 is a trapezoidal prism.
The total surface area of a trapezoidal prism is made up of 2 congruent trapezoid bases and 4 rectangular faces connecting the bases.
The formula for the area of a trapezoid is:
where a and b are the bases, and h is the height.
From observation of the given diagram, the bases are 16 ft and 19 ft, and the height is 12 ft. Therefore, the area of each trapezoid base is:
To calculate the areas of all the rectangular faces, we first need to calculate the slant (s) of the trapezoid base by using the Pythagoras Theorem:
The area of a rectangle is the product of its width and length.
Therefore, the sum of the areas of the rectangular faces is:
To find the total surface area of the given trapezoidal prism, sum the area of the two trapezoid bases and the area of the rectangular faces:
Therefore, the total surface area of the given trapezoidal prism is 1192 ft², rounded to the nearest foot.