# A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #2 # and #8 # and the pyramid's height is #2 #. If one of the base's corners has an angle of #(5pi)/6#, what is the pyramid's surface area?

##### 2 Answers

Total Surface Area # T S A = **34.8328**

#### Explanation:

Area of parallelogram base

Area of

Area of

Lateral surface area =

Total surface area =Area of parallelogram base + Lateral surface area

The pyramid's surface area is

#### Explanation:

I recommend to use coordinates to solve this problem.

The pyramid's base is ABCD and its center is E

The coordinates of A and B are:

In order to find the coordinates of C and D, we need to use trigonometry and the pythagorean theorem:

Therefore the coordinates of C and D are:

A parallelogram's diagonals cross mid-length, thus the coordinates of E are:

If the base is located in the (x;y) plane and the pyramid's peak (called F) is located at 2 above E, then the coordinates of all the pyramid's points are:

The pyramid's base's surface area is

The ADF and BCF sides' surface areas are:

The ABF and CDF sides' surface areas are:

Therefore, the pyramid's total surface area is: