Exercise 53 Page 870

The given solid is a pyramid.

To calculate the lateral area of a pyramid, we can use the known formula where $P$ is the perimeter of the base and $\ell$ is the slant height. The base of the pyramid is a square with the side length of $7\text{ cm}.$ Let's calculate its perimeter! We are also given that the slant height $\ell$ is $9\text{ cm}.$ Let's substitute all of these values into the formula for the lateral area and calculate it. We have found that the lateral area is $126{\text{ cm}}^2.$ To find the surface area, all we have to do is add the base area $B$ to the lateral area $L$. The base is a square with a side length of $7\text{ cm}.$ The area of the square equals the squared length of the side. We can now calculate the surface area. The surface area of the pyramid is $175{\text{ cm}}^2.$