Exercise 14 Page 904

Consider the given solid.

The given solid is a rectangular prism. It has a length of $11$ centimeters, a height of $3$ centimeters, and a width of $2$ centimeters. Let's first calculate the lateral area and then the surface area.

Lateral Area

To calculate the lateral area, we can use the known formula where $h$ is the height of the prism and $P$ is the perimeter of the base. We are given the length of the sides of the base. Let's calculate the perimeter of the base. The perimeter of the base is $26$ centimeters. We can substitute $P=26$ and $h=3$ in the formula to calculate $L.$ The lateral area is $78$ square centimeters.

Surface Area

To calculate the surface area of a prism, we can use the known formula where $P$ is the perimeter of the base, $h$ is the height, and $B$ is the area of the base. Note the base is a rectangle, so we can calculate its area using the formula for area of a rectangle. The area of the base is $22$ square centimeters. Earlier, we found that $Ph=78$ square centimeters. Let's substitute these values into the formula for the surface area of a prism. The surface area of the prism is $122$ square centimeters.