Pre-Algebra Examples

 $\begin{array}{r} h = & 2 \\ l = & 2.8 \\ w = & 3 \end{array}$

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 $l = 2.8$ , the width $w = 3$ , and the height $h = 2$ into the formula for surface area of a pyramid.

$2.8 \cdot 3 + 3 \cdot \sqrt{{(\frac{2.8}{2})}^{2} + {(2)}^{2}} + 2.8 \cdot \sqrt{{(\frac{3}{2})}^{2} + {(2)}^{2}}$

Step 3

Simplify each term.

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Step 3.1

Multiply $2.8$ by $3$ .

$8.4 + 3 \cdot \sqrt{{(\frac{2.8}{2})}^{2} + {(2)}^{2}} + 2.8 \cdot \sqrt{{(\frac{3}{2})}^{2} + {(2)}^{2}}$

Step 3.2

Divide $2.8$ by $2$ .

$8.4 + 3 \cdot \sqrt{{1.4}^{2} + {(2)}^{2}} + 2.8 \cdot \sqrt{{(\frac{3}{2})}^{2} + {(2)}^{2}}$

Step 3.3

Raise $1.4$ to the power of $2$ .

$8.4 + 3 \cdot \sqrt{1.96 + {(2)}^{2}} + 2.8 \cdot \sqrt{{(\frac{3}{2})}^{2} + {(2)}^{2}}$

Step 3.4

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

$8.4 + 3 \cdot \sqrt{1.96 + 4} + 2.8 \cdot \sqrt{{(\frac{3}{2})}^{2} + {(2)}^{2}}$

Step 3.5

Add $1.96$ and $4$ .

$8.4 + 3 \cdot \sqrt{5.96} + 2.8 \cdot \sqrt{{(\frac{3}{2})}^{2} + {(2)}^{2}}$

Step 3.6

Multiply $3$ by $\sqrt{5.96}$ .

$8.4 + 7.32393336 + 2.8 \cdot \sqrt{{(\frac{3}{2})}^{2} + {(2)}^{2}}$

Step 3.7

Cancel the common factor of $3$ and $2$ .

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Step 3.7.1

Rewrite $3$ as $1 (3)$ .

$8.4 + 7.32393336 + 2.8 \cdot \sqrt{{(\frac{1 (3)}{2})}^{2} + {(2)}^{2}}$

Step 3.7.2

Cancel the common factors.

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Step 3.7.2.1

Rewrite $2$ as $1 (2)$ .

$8.4 + 7.32393336 + 2.8 \cdot \sqrt{{(\frac{1 \cdot 3}{1 \cdot 2})}^{2} + {(2)}^{2}}$

Step 3.7.2.2

Cancel the common factor.

$8.4 + 7.32393336 + 2.8 \cdot \sqrt{{(\frac{1 \cdot 3}{1 \cdot 2})}^{2} + {(2)}^{2}}$

Step 3.7.2.3

Rewrite the expression.

$8.4 + 7.32393336 + 2.8 \cdot \sqrt{{(\frac{3}{2})}^{2} + {(2)}^{2}}$

Step 3.8

Apply the product rule to $\frac{3}{2}$ .

$8.4 + 7.32393336 + 2.8 \cdot \sqrt{\frac{3^{2}}{2^{2}} + {(2)}^{2}}$

Step 3.9

Raise $3$ to the power of $2$ .

$8.4 + 7.32393336 + 2.8 \cdot \sqrt{\frac{9}{2^{2}} + {(2)}^{2}}$

Step 3.10

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

$8.4 + 7.32393336 + 2.8 \cdot \sqrt{\frac{9}{4} + {(2)}^{2}}$

Step 3.11

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

$8.4 + 7.32393336 + 2.8 \cdot \sqrt{\frac{9}{4} + 4}$

Step 3.12

To write $4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$8.4 + 7.32393336 + 2.8 \cdot \sqrt{\frac{9}{4} + 4 \cdot \frac{4}{4}}$

Step 3.13

Combine $4$ and $\frac{4}{4}$ .

$8.4 + 7.32393336 + 2.8 \cdot \sqrt{\frac{9}{4} + \frac{4 \cdot 4}{4}}$

Step 3.14

Combine the numerators over the common denominator.

$8.4 + 7.32393336 + 2.8 \cdot \sqrt{\frac{9 + 4 \cdot 4}{4}}$

Step 3.15

Simplify the numerator.

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Step 3.15.1

Multiply $4$ by $4$ .

$8.4 + 7.32393336 + 2.8 \cdot \sqrt{\frac{9 + 16}{4}}$

Step 3.15.2

Add $9$ and $16$ .

$8.4 + 7.32393336 + 2.8 \cdot \sqrt{\frac{25}{4}}$

Step 3.16

Cancel the common factor of $25$ and $4$ .

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Step 3.16.1

Rewrite $25$ as $1 (25)$ .

$8.4 + 7.32393336 + 2.8 \cdot \sqrt{\frac{1 (25)}{4}}$

Step 3.16.2

Cancel the common factors.

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Step 3.16.2.1

Rewrite $4$ as $1 (4)$ .

$8.4 + 7.32393336 + 2.8 \cdot \sqrt{\frac{1 \cdot 25}{1 \cdot 4}}$

Step 3.16.2.2

Cancel the common factor.

$8.4 + 7.32393336 + 2.8 \cdot \sqrt{\frac{1 \cdot 25}{1 \cdot 4}}$

Step 3.16.2.3

Rewrite the expression.

$8.4 + 7.32393336 + 2.8 \cdot \sqrt{\frac{25}{4}}$

Step 3.17

Rewrite $\sqrt{\frac{25}{4}}$ as $\frac{\sqrt{25}}{\sqrt{4}}$ .

$8.4 + 7.32393336 + 2.8 \cdot \frac{\sqrt{25}}{\sqrt{4}}$

Step 3.18

Simplify the numerator.

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Step 3.18.1

Rewrite $25$ as $5^{2}$ .

$8.4 + 7.32393336 + 2.8 \cdot \frac{\sqrt{5^{2}}}{\sqrt{4}}$

Step 3.18.2

Pull terms out from under the radical, assuming positive real numbers.

$8.4 + 7.32393336 + 2.8 \cdot \frac{5}{\sqrt{4}}$

Step 3.19

Simplify the denominator.

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Step 3.19.1

Rewrite $4$ as $2^{2}$ .

$8.4 + 7.32393336 + 2.8 \cdot \frac{5}{\sqrt{2^{2}}}$

Step 3.19.2

Pull terms out from under the radical, assuming positive real numbers.

$8.4 + 7.32393336 + 2.8 \cdot \frac{5}{2}$

Step 3.20

Multiply $2.8 (\frac{5}{2})$ .

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Step 3.20.1

Combine $2.8$ and $\frac{5}{2}$ .

$8.4 + 7.32393336 + \frac{2.8 \cdot 5}{2}$

Step 3.20.2

Multiply $2.8$ by $5$ .

$8.4 + 7.32393336 + \frac{14}{2}$

Step 3.21

Divide $14$ by $2$ .

$8.4 + 7.32393336 + 7$

Step 4

Simplify by adding numbers.

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Step 4.1

Add $8.4$ and $7.32393336$ .

$15.72393336 + 7$

Step 4.2

Add $15.72393336$ and $7$ .

$22.72393336$

Step 5

Calculate the approximate solution to $4$ decimal places.

$22.7239$