Exercise 28 Page 66

Let's start by graphing the given box.

Since our box consists of 2 identical squares and 4 identical rectangles, we will write a formula for its surface area as the following sum. A_(Surface)=2A_(Square)+4A_(Rectangle)A_(Square) follows the standard formula for the area of a square. A square's height and length are the same, so multiplying them to find the area is the same as squaring. Let's substitute the given box measurements into it. A_(Square)= a^2 A_(Square)= 4^2=16 The A_(Rectangle) is similar to the standard formula for the area of a square, because it also is a function of length times height. We know one measurement of the rectangle, the length l, because it shares a side with the square. Let's substitute the given box measurements into it. A_(Rectangle)= l h A_(Rectangle)= 4 h Now, we will substitute what we have into the formula for surface area and simplify.

A_(Surface)=2A_(Square)+4A_(Rectangle)

SubstituteII

A_(Square)= 16, A_(Rectangle)= 4h

A_(Surface)=2( 16)+4( 4h)

Multiply

Multiply

A_(Surface)=32+16h

This is the function representing surface area we were looking for. Now, we can evaluate for h= 6.5

A_(Surface)=32+16h

Substitute

h= 6.5

A_(Surface)=32+16( 6.5)

Multiply

Multiply

A_(Surface)=32+104

AddTerms

Add terms

A_(Surface)=136

This means that the surface area of a box with 4* 4-in. base and a height of 6.5 in. is equal to 136in^2.