Basic Math Examples

 $\begin{array}{r} h = & 6.4 \\ l = & 8.2 \\ w = & 6.4 \end{array}$

Step 1

The surface area of a pyramid is equal to the sum of the areas of each side of the pyramid. The base of the pyramid has area $l w$ , and $s_{l}$ and $s_{w}$ represent the slant height on the length and slant height on the width.

$(l e n g t h) \cdot (w i d t h) + (w i d t h) \cdot s_{l} + (l e n g t h) \cdot s_{w}$

Step 2

Substitute the values of the length $l = 8.2$ , the width $w = 6.4$ , and the height $h = 6.4$ into the formula for surface area of a pyramid.

$8.2 \cdot 6.4 + 6.4 \cdot \sqrt{{(\frac{8.2}{2})}^{2} + {(6.4)}^{2}} + 8.2 \cdot \sqrt{{(\frac{6.4}{2})}^{2} + {(6.4)}^{2}}$

Step 3

Simplify each term.

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Step 3.1

Multiply $8.2$ by $6.4$ .

$52.48 + 6.4 \cdot \sqrt{{(\frac{8.2}{2})}^{2} + {(6.4)}^{2}} + 8.2 \cdot \sqrt{{(\frac{6.4}{2})}^{2} + {(6.4)}^{2}}$

Step 3.2

Divide $8.2$ by $2$ .

$52.48 + 6.4 \cdot \sqrt{{4.1}^{2} + {(6.4)}^{2}} + 8.2 \cdot \sqrt{{(\frac{6.4}{2})}^{2} + {(6.4)}^{2}}$

Step 3.3

Raise $4.1$ to the power of $2$ .

$52.48 + 6.4 \cdot \sqrt{16.81 + {(6.4)}^{2}} + 8.2 \cdot \sqrt{{(\frac{6.4}{2})}^{2} + {(6.4)}^{2}}$

Step 3.4

Raise $6.4$ to the power of $2$ .

$52.48 + 6.4 \cdot \sqrt{16.81 + 40.96} + 8.2 \cdot \sqrt{{(\frac{6.4}{2})}^{2} + {(6.4)}^{2}}$

Step 3.5

Add $16.81$ and $40.96$ .

$52.48 + 6.4 \cdot \sqrt{57.77} + 8.2 \cdot \sqrt{{(\frac{6.4}{2})}^{2} + {(6.4)}^{2}}$

Step 3.6

Multiply $6.4$ by $\sqrt{57.77}$ .

$52.48 + 48.64421034 + 8.2 \cdot \sqrt{{(\frac{6.4}{2})}^{2} + {(6.4)}^{2}}$

Step 3.7

Divide $6.4$ by $2$ .

$52.48 + 48.64421034 + 8.2 \cdot \sqrt{{3.2}^{2} + {(6.4)}^{2}}$

Step 3.8

Raise $3.2$ to the power of $2$ .

$52.48 + 48.64421034 + 8.2 \cdot \sqrt{10.24 + {(6.4)}^{2}}$

Step 3.9

Raise $6.4$ to the power of $2$ .

$52.48 + 48.64421034 + 8.2 \cdot \sqrt{10.24 + 40.96}$

Step 3.10

Add $10.24$ and $40.96$ .

$52.48 + 48.64421034 + 8.2 \cdot \sqrt{51.2}$

Step 3.11

Multiply $8.2$ by $\sqrt{51.2}$ .

$52.48 + 48.64421034 + 58.67442372$

Step 4

Simplify by adding numbers.

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Step 4.1

Add $52.48$ and $48.64421034$ .

$101.12421034 + 58.67442372$

Step 4.2

Add $101.12421034$ and $58.67442372$ .

$159.79863407$

Step 5

Calculate the approximate solution to $4$ decimal places.

$159.7986$