Basic Math Examples



\begin{matrix} h = & 3 l = & 2 w = & 4 \end{matrix}

$\begin{array}{r} h = & 3 \\ l = & 2 \\ w = & 4 \end{array}$

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 = 2

$l = 2$ , the width

w = 4

$w = 4$ , and the height

h = 3

$h = 3$ into the formula.

2 \cdot 2 \cdot 4 + 2 \cdot 2 \cdot 3 + 2 \cdot 4 \cdot 3

$2 \cdot 2 \cdot 4 + 2 \cdot 2 \cdot 3 + 2 \cdot 4 \cdot 3$

Step 3

Simplify each term.

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Step 3.1

Multiply

2 \cdot 2 \cdot 4

$2 \cdot 2 \cdot 4$ .

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Step 3.1.1

Multiply

2

$2$ by

2

$2$ .

4 \cdot 4 + 2 \cdot 2 \cdot 3 + 2 \cdot 4 \cdot 3

$4 \cdot 4 + 2 \cdot 2 \cdot 3 + 2 \cdot 4 \cdot 3$

Step 3.1.2

Multiply

4

$4$ by

4

$4$ .

16 + 2 \cdot 2 \cdot 3 + 2 \cdot 4 \cdot 3

$16 + 2 \cdot 2 \cdot 3 + 2 \cdot 4 \cdot 3$

16 + 2 \cdot 2 \cdot 3 + 2 \cdot 4 \cdot 3

$16 + 2 \cdot 2 \cdot 3 + 2 \cdot 4 \cdot 3$

Step 3.2

Multiply

2 \cdot 2 \cdot 3

$2 \cdot 2 \cdot 3$ .

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Step 3.2.1

Multiply

2

$2$ by

2

$2$ .

16 + 4 \cdot 3 + 2 \cdot 4 \cdot 3

$16 + 4 \cdot 3 + 2 \cdot 4 \cdot 3$

Step 3.2.2

Multiply

4

$4$ by

3

$3$ .

16 + 12 + 2 \cdot 4 \cdot 3

$16 + 12 + 2 \cdot 4 \cdot 3$

16 + 12 + 2 \cdot 4 \cdot 3

$16 + 12 + 2 \cdot 4 \cdot 3$

Step 3.3

Multiply

2 \cdot 4 \cdot 3

$2 \cdot 4 \cdot 3$ .

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Step 3.3.1

Multiply

2

$2$ by

4

$4$ .

16 + 12 + 8 \cdot 3

$16 + 12 + 8 \cdot 3$

Step 3.3.2

Multiply

8

$8$ by

3

$3$ .

16 + 12 + 24

$16 + 12 + 24$

16 + 12 + 24

$16 + 12 + 24$

16 + 12 + 24

$16 + 12 + 24$

Step 4

Simplify by adding numbers.

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Step 4.1

Add

16

$16$ and

12

$12$ .

28 + 24

$28 + 24$

Step 4.2

Add

28

$28$ and

24

$24$ .

52

$52$

52

$52$