Pre-Algebra Examples



\begin{array}{r} h = & 6 \\ l = & 5 \\ w = & 5 \end{array}

$\begin{array}{r} h = & 6 \\ l = & 5 \\ w = & 5 \end{array}$

Step 1

The surface area of a box is equal to the sum of the areas of each side of the box.

2 \cdot (l e n g t h) \cdot (w i d t h) + 2 \cdot (l e n g t h) \cdot (h e i g h t) + 2 \cdot (w i d t h) \cdot (h e i g h t)

$2 \cdot (l e n g t h) \cdot (w i d t h) + 2 \cdot (l e n g t h) \cdot (h e i g h t) + 2 \cdot (w i d t h) \cdot (h e i g h t)$

Step 2

Substitute the values of the length

l = 5

$l = 5$ , the width

w = 5

$w = 5$ , and the height

h = 6

$h = 6$ into the formula.

2 \cdot 5 \cdot 5 + 2 \cdot 5 \cdot 6 + 2 \cdot 5 \cdot 6

$2 \cdot 5 \cdot 5 + 2 \cdot 5 \cdot 6 + 2 \cdot 5 \cdot 6$

Step 3

Simplify each term.

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Step 3.1

Multiply

2 \cdot 5 \cdot 5

$2 \cdot 5 \cdot 5$ .

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Step 3.1.1

Multiply

2

$2$ by

5

$5$ .

10 \cdot 5 + 2 \cdot 5 \cdot 6 + 2 \cdot 5 \cdot 6

$10 \cdot 5 + 2 \cdot 5 \cdot 6 + 2 \cdot 5 \cdot 6$

Step 3.1.2

Multiply

10

$10$ by

5

$5$ .

50 + 2 \cdot 5 \cdot 6 + 2 \cdot 5 \cdot 6

$50 + 2 \cdot 5 \cdot 6 + 2 \cdot 5 \cdot 6$

50 + 2 \cdot 5 \cdot 6 + 2 \cdot 5 \cdot 6

$50 + 2 \cdot 5 \cdot 6 + 2 \cdot 5 \cdot 6$

Step 3.2

Multiply

2 \cdot 5 \cdot 6

$2 \cdot 5 \cdot 6$ .

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Step 3.2.1

Multiply

2

$2$ by

5

$5$ .

50 + 10 \cdot 6 + 2 \cdot 5 \cdot 6

$50 + 10 \cdot 6 + 2 \cdot 5 \cdot 6$

Step 3.2.2

Multiply

10

$10$ by

6

$6$ .

50 + 60 + 2 \cdot 5 \cdot 6

$50 + 60 + 2 \cdot 5 \cdot 6$

50 + 60 + 2 \cdot 5 \cdot 6

$50 + 60 + 2 \cdot 5 \cdot 6$

Step 3.3

Multiply

2 \cdot 5 \cdot 6

$2 \cdot 5 \cdot 6$ .

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Step 3.3.1

Multiply

2

$2$ by

5

$5$ .

50 + 60 + 10 \cdot 6

$50 + 60 + 10 \cdot 6$

Step 3.3.2

Multiply

10

$10$ by

6

$6$ .

50 + 60 + 60

$50 + 60 + 60$

50 + 60 + 60

$50 + 60 + 60$

50 + 60 + 60

$50 + 60 + 60$

Step 4

Simplify by adding numbers.

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Step 4.1

Add

50

$50$ and

60

$60$ .

110 + 60

$110 + 60$

Step 4.2

Add

110

$110$ and

60

$60$ .

170

$170$

170

$170$