Basic Math Examples

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\begin{array}{r} h = & 3 \\ l = & 1 \\ w = & 6 \end{array}

$\begin{array}{r} h = & 3 \\ l = & 1 \\ w = & 6 \end{array}$

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 = 1

$l = 1$ , the width

w = 6

$w = 6$ , and the height

h = 3

$h = 3$ into the formula.

2 \cdot 1 \cdot 6 + 2 \cdot 1 \cdot 3 + 2 \cdot 6 \cdot 3

$2 \cdot 1 \cdot 6 + 2 \cdot 1 \cdot 3 + 2 \cdot 6 \cdot 3$

Step 3

Simplify each term.

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Step 3.1

Multiply

2 \cdot 1 \cdot 6

$2 \cdot 1 \cdot 6$ .

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Step 3.1.1

Multiply

2

$2$ by

1

$1$ .

2 \cdot 6 + 2 \cdot 1 \cdot 3 + 2 \cdot 6 \cdot 3

$2 \cdot 6 + 2 \cdot 1 \cdot 3 + 2 \cdot 6 \cdot 3$

Step 3.1.2

Multiply

2

$2$ by

6

$6$ .

12 + 2 \cdot 1 \cdot 3 + 2 \cdot 6 \cdot 3

$12 + 2 \cdot 1 \cdot 3 + 2 \cdot 6 \cdot 3$

12 + 2 \cdot 1 \cdot 3 + 2 \cdot 6 \cdot 3

$12 + 2 \cdot 1 \cdot 3 + 2 \cdot 6 \cdot 3$

Step 3.2

Multiply

2 \cdot 1 \cdot 3

$2 \cdot 1 \cdot 3$ .

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Step 3.2.1

Multiply

2

$2$ by

1

$1$ .

12 + 2 \cdot 3 + 2 \cdot 6 \cdot 3

$12 + 2 \cdot 3 + 2 \cdot 6 \cdot 3$

Step 3.2.2

Multiply

2

$2$ by

3

$3$ .

12 + 6 + 2 \cdot 6 \cdot 3

$12 + 6 + 2 \cdot 6 \cdot 3$

12 + 6 + 2 \cdot 6 \cdot 3

$12 + 6 + 2 \cdot 6 \cdot 3$

Step 3.3

Multiply

2 \cdot 6 \cdot 3

$2 \cdot 6 \cdot 3$ .

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Step 3.3.1

Multiply

2

$2$ by

6

$6$ .

12 + 6 + 12 \cdot 3

$12 + 6 + 12 \cdot 3$

Step 3.3.2

Multiply

12

$12$ by

3

$3$ .

12 + 6 + 36

$12 + 6 + 36$

12 + 6 + 36

$12 + 6 + 36$

12 + 6 + 36

$12 + 6 + 36$

Step 4

Simplify by adding numbers.

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Step 4.1

Add

12

$12$ and

6

$6$ .

18 + 36

$18 + 36$

Step 4.2

Add

18

$18$ and

36

$36$ .

54

$54$

54

$54$

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