a Look at the figure carefully to find an expression that takes into account the area of each of its sides.
B
b Solve for h from the surface area formula found in Part A. Then, substitute the given values for the area and the base side.
C
c Look at the figure, what would happen when h=s? Substitute h=s in the surface area formula and simplify.
A
a A = 2s^2 + 4hs
B
bFormula for h in Terms of A and s: h = A - 2s^2/4s Height of the Prism: 14cm
C
c A = 6s^2
Practice makes perfect
a We are given a rectangular prism with height h and square bases with side length s, as shown in the figure below. Let's find a formula for its surface area!
From the figure, we can see that as the base is a square of side s, its area will be given as s * s = s^2. Notice we will have 2 of these. Also, we have 4 rectangular, lateral sides of base s and length h. Their area will be given by h * s. Then, the total surface area will be given by the expression A = 2s^2 + 4hs.
b Now, we want to rewrite the surface area formula to find h in terms of A and s. In Part A, we found that the surface area is given by A = 2s^2 + 4hs. Let's solve for h using inverse operations.
Now that we found the expression for h, we can determine the height if the prism were to have an area of 760 cm^2 and a base side length of s=10cm. Let's substitute these values in our formula and simplify.
c Next, we can rewrite the formula from Part A to see what it would look like in terms of s for the case when h=s. Let's substitute h=s in the formula and simplify.
