find the surface area of isosceles trapezoidal prism given the measures shown. note that the figure is not…

Explanation:

Step1: Calculate base trapezoid area

The area of a trapezoid is $\frac{1}{2} \times (a + b) \times h$, where $a=12$, $b=36$, $h=16$. $\text{Area of 1 trapezoid} = \frac{1}{2} \times (12 + 36) \times 16 = \frac{1}{2} \times 48 \times 16 = 384$ Total area of 2 trapezoids: $2 \times 384 = 768$

Step2: Calculate rectangle areas

There are 3 rectangular faces:

1. Rectangle 1: $36 \times 20 = 720$
2. Rectangle 2: $12 \times 20 = 240$
3. Two congruent rectangles: First find the leg of the trapezoid using Pythagoras: $\sqrt{16^2 + \left(\frac{36-12}{2}\right)^2} = \sqrt{256 + 144} = \sqrt{400} = 20$. Area of one: $20 \times 20 = 400$, total for two: $2 \times 400 = 800$

Step3: Sum all surface areas

Add the areas from Step1 and Step2. $\text{Total Surface Area} = 768 + 720 + 240 + 800$

Answer:

2528