Exercise 35 Page 820

Let's analyze the given solid. It can be viewed as a quadrangular prism with the base in a shape of a trapezoid and a height of h= 28 centimeters.

We are asked to find the surface area of the prism S. S= P h+2 B Here, P is the perimeter of the base and B is the area of the base. The base is a trapezoid with bases b_1=20 cm and b_2=13 cm, and the height is \textcolor{darkviolet}{h_\text{base}}=\textcolor{darkviolet}{21} cm. Let's find its area B using the formula for the area of a trapezoid.

Therefore, the area of the base is B=346.5 square centimeters. Now, let's find the perimeter of the base.

Notice that AB=20-13=7 centimeters and AC=21 centimeters. Let's use the Pythagorean Theorem for right △ ABC to find BC.

Now, let's find the perimeter of the base. P=20+21+13+22.14= 76.14 Finally, let's substitute known values into the formula for the surface area of the given solid.

This tells us that the surface area is about 2824.9 square centimeters.