# 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 #2 #, its base's sides have lengths of #4 #, and its base has a corner with an angle of #( pi)/4 #. What is the pyramid's surface area?

T S A = 33.9409

AB = BC = CD = DA = a = 4

Height OE = h = 2

OF = a/2 = 4/2 = 2

Area of

Lateral surface area

Area of base ABCD

T S A

T S A

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The surface area of the pyramid can be calculated by adding the area of the base to the sum of the areas of the four triangular faces.

The area of the base rhombus can be found using the formula (A_{\text{base}} = s^2), where (s) is the length of one side of the rhombus.

The area of each triangular face can be calculated using the formula (A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}), where the base of each triangle is the side length of the rhombus, and the height is the height of the pyramid.

Given:

- Side length of the base rhombus ((s)) = 4
- Height of the pyramid ((h)) = 2

First, calculate the area of the base rhombus ((A_{\text{base}})) using the given side length.

Next, calculate the area of each triangular face ((A_{\text{triangle}})) using the given side length and height.

Finally, sum the area of the base rhombus with four times the area of each triangular face to find the total surface area of the pyramid.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- The base of a triangular pyramid is a triangle with corners at #(5 ,8 )#, #(4 ,1 )#, and #(9 ,3 )#. If the pyramid has a height of #4 #, what is the pyramid's volume?
- Two corners of a triangle have angles of #(3 pi ) / 4 # and # pi / 6 #. If one side of the triangle has a length of #6 #, what is the longest possible perimeter of the triangle?
- A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #33 # and the height of the cylinder is #14 #. If the volume of the solid is #70 pi#, what is the area of the base of the cylinder?
- A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #2 # and #1 # and the pyramid's height is #7 #. If one of the base's corners has an angle of #(5pi)/6#, what is the pyramid's surface area?
- Find the area of a parallelogram with a base of 6 cm and a height of 11 cm?

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