Question

find the surface area of the trapezoidal prism.
sa = \square square inches

Explanation:

Step1: Find area of trapezoidal bases

The formula for the area of a trapezoid is $A = \frac{(a + b)}{2} \times h$, where $a = 16$ in, $b = 10$ in, $h = 4$ in.
$A_{base} = \frac{(16 + 10)}{2} \times 4 = \frac{26}{2} \times 4 = 13 \times 4 = 52$ square inches.
Since there are two bases, total area of bases is $2 \times 52 = 104$ square inches.

Step2: Find area of rectangular faces

• Face 1: Dimensions 16 in and 5 in. Area = $16 \times 5 = 80$ square inches.
• Face 2: Dimensions 10 in and 5 in. Area = $10 \times 5 = 50$ square inches.
• Face 3: Dimensions 10 in and 5 in. Area = $10 \times 5 = 50$ square inches.

Total area of rectangular faces = $80 + 50 + 50 = 180$ square inches.

Step3: Sum all areas

Surface area $SA =$ area of bases + area of rectangular faces = $104 + 180 = 284$ square inches.

Answer:

284