Pre-Algebra Examples

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\begin{matrix} h = & 9 l = & 5 w = & 4 \end{matrix}

$\begin{array}{r} h = & 9 \\ l = & 5 \\ w = & 4 \end{array}$

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 = 4

$w = 4$ , and the height

h = 9

$h = 9$ into the formula.

2 \cdot 5 \cdot 4 + 2 \cdot 5 \cdot 9 + 2 \cdot 4 \cdot 9

$2 \cdot 5 \cdot 4 + 2 \cdot 5 \cdot 9 + 2 \cdot 4 \cdot 9$

Step 3

Simplify each term.

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Step 3.1

Multiply

2 \cdot 5 \cdot 4

$2 \cdot 5 \cdot 4$ .

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Step 3.1.1

Multiply

2

$2$ by

5

$5$ .

10 \cdot 4 + 2 \cdot 5 \cdot 9 + 2 \cdot 4 \cdot 9

$10 \cdot 4 + 2 \cdot 5 \cdot 9 + 2 \cdot 4 \cdot 9$

Step 3.1.2

Multiply

10

$10$ by

4

$4$ .

40 + 2 \cdot 5 \cdot 9 + 2 \cdot 4 \cdot 9

$40 + 2 \cdot 5 \cdot 9 + 2 \cdot 4 \cdot 9$

40 + 2 \cdot 5 \cdot 9 + 2 \cdot 4 \cdot 9

$40 + 2 \cdot 5 \cdot 9 + 2 \cdot 4 \cdot 9$

Step 3.2

Multiply

2 \cdot 5 \cdot 9

$2 \cdot 5 \cdot 9$ .

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Step 3.2.1

Multiply

2

$2$ by

5

$5$ .

40 + 10 \cdot 9 + 2 \cdot 4 \cdot 9

$40 + 10 \cdot 9 + 2 \cdot 4 \cdot 9$

Step 3.2.2

Multiply

10

$10$ by

9

$9$ .

40 + 90 + 2 \cdot 4 \cdot 9

$40 + 90 + 2 \cdot 4 \cdot 9$

40 + 90 + 2 \cdot 4 \cdot 9

$40 + 90 + 2 \cdot 4 \cdot 9$

Step 3.3

Multiply

2 \cdot 4 \cdot 9

$2 \cdot 4 \cdot 9$ .

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Step 3.3.1

Multiply

2

$2$ by

4

$4$ .

40 + 90 + 8 \cdot 9

$40 + 90 + 8 \cdot 9$

Step 3.3.2

Multiply

8

$8$ by

9

$9$ .

40 + 90 + 72

$40 + 90 + 72$

40 + 90 + 72

$40 + 90 + 72$

40 + 90 + 72

$40 + 90 + 72$

Step 4

Simplify by adding numbers.

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Step 4.1

Add

40

$40$ and

90

$90$ .

130 + 72

$130 + 72$

Step 4.2

Add

130

$130$ and

72

$72$ .

202

$202$

202

$202$

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