Pre-Algebra Examples

 $\begin{array}{r} h = & 4.8 \\ l = & 5.5 \\ w = & 1.4 \end{array}$

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 $l = 5.5$ , the width $w = 1.4$ , and the height $h = 4.8$ into the formula for surface area of a pyramid.

$5.5 \cdot 1.4 + 1.4 \cdot \sqrt{{(\frac{5.5}{2})}^{2} + {(4.8)}^{2}} + 5.5 \cdot \sqrt{{(\frac{1.4}{2})}^{2} + {(4.8)}^{2}}$

Step 3

Simplify each term.

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Step 3.1

Multiply $5.5$ by $1.4$ .

$7.7 + 1.4 \cdot \sqrt{{(\frac{5.5}{2})}^{2} + {(4.8)}^{2}} + 5.5 \cdot \sqrt{{(\frac{1.4}{2})}^{2} + {(4.8)}^{2}}$

Step 3.2

Divide $5.5$ by $2$ .

$7.7 + 1.4 \cdot \sqrt{{2.75}^{2} + {(4.8)}^{2}} + 5.5 \cdot \sqrt{{(\frac{1.4}{2})}^{2} + {(4.8)}^{2}}$

Step 3.3

Raise $2.75$ to the power of $2$ .

$7.7 + 1.4 \cdot \sqrt{7.5625 + {(4.8)}^{2}} + 5.5 \cdot \sqrt{{(\frac{1.4}{2})}^{2} + {(4.8)}^{2}}$

Step 3.4

Raise $4.8$ to the power of $2$ .

$7.7 + 1.4 \cdot \sqrt{7.5625 + 23.04} + 5.5 \cdot \sqrt{{(\frac{1.4}{2})}^{2} + {(4.8)}^{2}}$

Step 3.5

Add $7.5625$ and $23.04$ .

$7.7 + 1.4 \cdot \sqrt{30.6025} + 5.5 \cdot \sqrt{{(\frac{1.4}{2})}^{2} + {(4.8)}^{2}}$

Step 3.6

Multiply $1.4$ by $\sqrt{30.6025}$ .

$7.7 + 7.74473369 + 5.5 \cdot \sqrt{{(\frac{1.4}{2})}^{2} + {(4.8)}^{2}}$

Step 3.7

Divide $1.4$ by $2$ .

$7.7 + 7.74473369 + 5.5 \cdot \sqrt{{0.7}^{2} + {(4.8)}^{2}}$

Step 3.8

Raise $0.7$ to the power of $2$ .

$7.7 + 7.74473369 + 5.5 \cdot \sqrt{0.49 + {(4.8)}^{2}}$

Step 3.9

Raise $4.8$ to the power of $2$ .

$7.7 + 7.74473369 + 5.5 \cdot \sqrt{0.49 + 23.04}$

Step 3.10

Add $0.49$ and $23.04$ .

$7.7 + 7.74473369 + 5.5 \cdot \sqrt{23.53}$

Step 3.11

Multiply $5.5$ by $\sqrt{23.53}$ .

$7.7 + 7.74473369 + 26.67925223$

Step 4

Simplify by adding numbers.

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Step 4.1

Add $7.7$ and $7.74473369$ .

$15.44473369 + 26.67925223$

Step 4.2

Add $15.44473369$ and $26.67925223$ .

$42.12398593$

Step 5

Calculate the approximate solution to $4$ decimal places.

$42.124$