Basic Math Examples

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\begin{array}{r} h = & 5 \\ l = & 3 \\ w = & 2 \end{array}

$\begin{array}{r} h = & 5 \\ l = & 3 \\ w = & 2 \end{array}$

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 = 3

$l = 3$ , the width

w = 2

$w = 2$ , and the height

h = 5

$h = 5$ into the formula.

2 \cdot 3 \cdot 2 + 2 \cdot 3 \cdot 5 + 2 \cdot 2 \cdot 5

$2 \cdot 3 \cdot 2 + 2 \cdot 3 \cdot 5 + 2 \cdot 2 \cdot 5$

Step 3

Simplify each term.

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Step 3.1

Multiply

2 \cdot 3 \cdot 2

$2 \cdot 3 \cdot 2$ .

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Step 3.1.1

Multiply

2

$2$ by

3

$3$ .

6 \cdot 2 + 2 \cdot 3 \cdot 5 + 2 \cdot 2 \cdot 5

$6 \cdot 2 + 2 \cdot 3 \cdot 5 + 2 \cdot 2 \cdot 5$

Step 3.1.2

Multiply

6

$6$ by

2

$2$ .

12 + 2 \cdot 3 \cdot 5 + 2 \cdot 2 \cdot 5

$12 + 2 \cdot 3 \cdot 5 + 2 \cdot 2 \cdot 5$

12 + 2 \cdot 3 \cdot 5 + 2 \cdot 2 \cdot 5

$12 + 2 \cdot 3 \cdot 5 + 2 \cdot 2 \cdot 5$

Step 3.2

Multiply

2 \cdot 3 \cdot 5

$2 \cdot 3 \cdot 5$ .

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Step 3.2.1

Multiply

2

$2$ by

3

$3$ .

12 + 6 \cdot 5 + 2 \cdot 2 \cdot 5

$12 + 6 \cdot 5 + 2 \cdot 2 \cdot 5$

Step 3.2.2

Multiply

6

$6$ by

5

$5$ .

12 + 30 + 2 \cdot 2 \cdot 5

$12 + 30 + 2 \cdot 2 \cdot 5$

12 + 30 + 2 \cdot 2 \cdot 5

$12 + 30 + 2 \cdot 2 \cdot 5$

Step 3.3

Multiply

2 \cdot 2 \cdot 5

$2 \cdot 2 \cdot 5$ .

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Step 3.3.1

Multiply

2

$2$ by

2

$2$ .

12 + 30 + 4 \cdot 5

$12 + 30 + 4 \cdot 5$

Step 3.3.2

Multiply

4

$4$ by

5

$5$ .

12 + 30 + 20

$12 + 30 + 20$

12 + 30 + 20

$12 + 30 + 20$

12 + 30 + 20

$12 + 30 + 20$

Step 4

Simplify by adding numbers.

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Step 4.1

Add

12

$12$ and

30

$30$ .

42 + 20

$42 + 20$

Step 4.2

Add

42

$42$ and

20

$20$ .

62

$62$

62

$62$