Find the Surface Area pyramid (8)(8)(10)



$\begin{array}{r} h = & 8 \\ l = & 10 \\ w = & 8 \end{array}$

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

$l = 10$ , the width

$w = 8$ , and the height

$h = 8$ into the formula for surface area of a pyramid.

$10 \cdot 8 + 8 \cdot \sqrt{{(\frac{10}{2})}^{2} + {(8)}^{2}} + 10 \cdot \sqrt{{(\frac{8}{2})}^{2} + {(8)}^{2}}$

Step 3

Simplify each term.

Multiply

$10$ by

$8$ .

$80 + 8 \cdot \sqrt{{(\frac{10}{2})}^{2} + {(8)}^{2}} + 10 \cdot \sqrt{{(\frac{8}{2})}^{2} + {(8)}^{2}}$

Divide

$10$ by

$2$ .

$80 + 8 \cdot \sqrt{5^{2} + {(8)}^{2}} + 10 \cdot \sqrt{{(\frac{8}{2})}^{2} + {(8)}^{2}}$

Raise

$5$ to the power of

$2$ .

$80 + 8 \cdot \sqrt{25 + {(8)}^{2}} + 10 \cdot \sqrt{{(\frac{8}{2})}^{2} + {(8)}^{2}}$

Raise

$8$ to the power of

$2$ .

$80 + 8 \cdot \sqrt{25 + 64} + 10 \cdot \sqrt{{(\frac{8}{2})}^{2} + {(8)}^{2}}$

Add

$25$ and

$64$ .

$80 + 8 \cdot \sqrt{89} + 10 \cdot \sqrt{{(\frac{8}{2})}^{2} + {(8)}^{2}}$

Divide

$8$ by

$2$ .

$80 + 8 \sqrt{89} + 10 \cdot \sqrt{4^{2} + {(8)}^{2}}$

Raise

$4$ to the power of

$2$ .

$80 + 8 \sqrt{89} + 10 \cdot \sqrt{16 + {(8)}^{2}}$

Raise

$8$ to the power of

$2$ .

$80 + 8 \sqrt{89} + 10 \cdot \sqrt{16 + 64}$

Add

$16$ and

$64$ .

$80 + 8 \sqrt{89} + 10 \cdot \sqrt{80}$

Rewrite

$80$ as

$4^{2} \cdot 5$ .

Factor

$16$ out of

$80$ .

$80 + 8 \sqrt{89} + 10 \cdot \sqrt{16 (5)}$

Rewrite

$16$ as

$4^{2}$ .

$80 + 8 \sqrt{89} + 10 \cdot \sqrt{4^{2} \cdot 5}$

Pull terms out from under the radical.

$80 + 8 \sqrt{89} + 10 \cdot (4 \sqrt{5})$

Multiply

$4$ by

$10$ .

$80 + 8 \sqrt{89} + 40 \sqrt{5}$

Step 4

Calculate the approximate solution to

$4$ decimal places.

$244.9146$

Find the Surface Area pyramid (8)(8)(10)

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