Let's recall the formula for the surface area of a prism S.
S=Ph+2B
Here, P is the perimeter of the base, h is the height, and B is the area of the base. Let's start by finding the perimeter of the base. We know that the base is a rectangle with length 15cm and width 4cm. Its perimeter is twice the sum of these two numbers.
P=2( 15+ 4) ⇔ P = 38cm
Now, we can calculate the area of the base using the formula for the area of a rectangle.
The area of the base is 60cm^2. We also know that the surface area of the solid is 310cm^2. With this information, we can find the height of the prism.
