# A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is 8 , its base has sides of length 3 , and its base has a corner with an angle of  pi/3 . What is the pyramid's surface area?

Jun 29, 2018

#### Answer:

color(cyan)(T S A = 56.63 " sq units"

#### Explanation:

"Area of rhombus base ' + A_r = s^2 * sin (pi/3) = 3^2 * (sqrt3/2) = 7.79

$\text{Slant height of the pyramid } l = \sqrt{{\left(\frac{3}{2}\right)}^{2} + {8}^{2}} = 8.1394$

$\text{Lateral Surface Area of Pyramid } L S A = 4 \cdot \left(\frac{1}{2}\right) \cdot s \cdot l$

$L S A = 4 \cdot \left(\frac{1}{2}\right) \cdot 3 \cdot 8.1394 = 48.84$

"Total Surface Area of Pyramid ' = T S A = A_b + L S A

$T S A = 7.79 + 48.84 = 56.63 \text{ sq units}$