Find the Surface Area pyramid (8)(5)(3)

 $\begin{array}{r} h = & 8 \\ l = & 3 \\ w = & 5 \end{array}$

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.

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

Substitute the values of the length $l = 3$ , the width $w = 5$ , and the height $h = 8$ into the formula for surface area of a pyramid.

$3 \cdot 5 + 5 \cdot \sqrt{{(\frac{3}{2})}^{2} + {(8)}^{2}} + 3 \cdot \sqrt{{(\frac{5}{2})}^{2} + {(8)}^{2}}$

Simplify each term.

Tap for more steps…

Multiply $3$ by $5$ .

$15 + 5 \cdot \sqrt{{(\frac{3}{2})}^{2} + {(8)}^{2}} + 3 \cdot \sqrt{{(\frac{5}{2})}^{2} + {(8)}^{2}}$

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

$15 + 5 \cdot \sqrt{\frac{3^{2}}{2^{2}} + {(8)}^{2}} + 3 \cdot \sqrt{{(\frac{5}{2})}^{2} + {(8)}^{2}}$

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

$15 + 5 \cdot \sqrt{\frac{9}{2^{2}} + {(8)}^{2}} + 3 \cdot \sqrt{{(\frac{5}{2})}^{2} + {(8)}^{2}}$

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

$15 + 5 \cdot \sqrt{\frac{9}{4} + {(8)}^{2}} + 3 \cdot \sqrt{{(\frac{5}{2})}^{2} + {(8)}^{2}}$

Raise $8$ to the power of $2$ .

$15 + 5 \cdot \sqrt{\frac{9}{4} + 64} + 3 \cdot \sqrt{{(\frac{5}{2})}^{2} + {(8)}^{2}}$

To write $64$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$15 + 5 \cdot \sqrt{\frac{9}{4} + 64 \cdot \frac{4}{4}} + 3 \cdot \sqrt{{(\frac{5}{2})}^{2} + {(8)}^{2}}$

Combine $64$ and $\frac{4}{4}$ .

$15 + 5 \cdot \sqrt{\frac{9}{4} + \frac{64 \cdot 4}{4}} + 3 \cdot \sqrt{{(\frac{5}{2})}^{2} + {(8)}^{2}}$

Combine the numerators over the common denominator.

$15 + 5 \cdot \sqrt{\frac{9 + 64 \cdot 4}{4}} + 3 \cdot \sqrt{{(\frac{5}{2})}^{2} + {(8)}^{2}}$

Simplify the numerator.

Tap for more steps…

Multiply $64$ by $4$ .

$15 + 5 \cdot \sqrt{\frac{9 + 256}{4}} + 3 \cdot \sqrt{{(\frac{5}{2})}^{2} + {(8)}^{2}}$

Add $9$ and $256$ .

$15 + 5 \cdot \sqrt{\frac{265}{4}} + 3 \cdot \sqrt{{(\frac{5}{2})}^{2} + {(8)}^{2}}$

Rewrite $\sqrt{\frac{265}{4}}$ as $\frac{\sqrt{265}}{\sqrt{4}}$ .

$15 + 5 \cdot \frac{\sqrt{265}}{\sqrt{4}} + 3 \cdot \sqrt{{(\frac{5}{2})}^{2} + {(8)}^{2}}$

Simplify the denominator.

Tap for more steps…

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

$15 + 5 \cdot \frac{\sqrt{265}}{\sqrt{2^{2}}} + 3 \cdot \sqrt{{(\frac{5}{2})}^{2} + {(8)}^{2}}$

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

$15 + 5 \cdot \frac{\sqrt{265}}{2} + 3 \cdot \sqrt{{(\frac{5}{2})}^{2} + {(8)}^{2}}$

$15 + \frac{5 \sqrt{265}}{2} + 3 \cdot \sqrt{{(\frac{5}{2})}^{2} + {(8)}^{2}}$

Apply the product rule to $\frac{5}{2}$ .

$15 + \frac{5 \sqrt{265}}{2} + 3 \cdot \sqrt{\frac{5^{2}}{2^{2}} + {(8)}^{2}}$

Raise $5$ to the power of $2$ .

$15 + \frac{5 \sqrt{265}}{2} + 3 \cdot \sqrt{\frac{25}{2^{2}} + {(8)}^{2}}$

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

$15 + \frac{5 \sqrt{265}}{2} + 3 \cdot \sqrt{\frac{25}{4} + {(8)}^{2}}$

Raise $8$ to the power of $2$ .

$15 + \frac{5 \sqrt{265}}{2} + 3 \cdot \sqrt{\frac{25}{4} + 64}$

To write $64$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$15 + \frac{5 \sqrt{265}}{2} + 3 \cdot \sqrt{\frac{25}{4} + 64 \cdot \frac{4}{4}}$

Combine $64$ and $\frac{4}{4}$ .

$15 + \frac{5 \sqrt{265}}{2} + 3 \cdot \sqrt{\frac{25}{4} + \frac{64 \cdot 4}{4}}$

Combine the numerators over the common denominator.

$15 + \frac{5 \sqrt{265}}{2} + 3 \cdot \sqrt{\frac{25 + 64 \cdot 4}{4}}$

Simplify the numerator.

Tap for more steps…

Multiply $64$ by $4$ .

$15 + \frac{5 \sqrt{265}}{2} + 3 \cdot \sqrt{\frac{25 + 256}{4}}$

Add $25$ and $256$ .

$15 + \frac{5 \sqrt{265}}{2} + 3 \cdot \sqrt{\frac{281}{4}}$

Rewrite $\sqrt{\frac{281}{4}}$ as $\frac{\sqrt{281}}{\sqrt{4}}$ .

$15 + \frac{5 \sqrt{265}}{2} + 3 \cdot \frac{\sqrt{281}}{\sqrt{4}}$

Simplify the denominator.

Tap for more steps…

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

$15 + \frac{5 \sqrt{265}}{2} + 3 \cdot \frac{\sqrt{281}}{\sqrt{2^{2}}}$

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

$15 + \frac{5 \sqrt{265}}{2} + 3 \cdot \frac{\sqrt{281}}{2}$

$15 + \frac{5 \sqrt{265}}{2} + \frac{3 \sqrt{281}}{2}$

Calculate the approximate solution to $4$ decimal places.

$80.8416$

Find the Surface Area pyramid (8)(5)(3)

Meet the Team our Math Expers

Our Professionals

Robert Kristofer

Anna Frok

Magnus Flores

Lydia Fran

We are MathExperts

We can solve all your math problems