# 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)/6 #. What is the pyramid's surface area?

T S A

Pyramid total surface area = base area + lateral surface area

Base is a rhombus and hence

Lateral Surface area

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The surface area of the pyramid can be calculated by finding the sum of the areas of its base and its four triangular faces.

Given that the base of the pyramid is a rhombus with side length ( s = 4 ) and an angle of ( \frac{\pi}{6} ) at one of its corners, the area of the base can be calculated using the formula for the area of a rhombus: ( A_{\text{base}} = s^2 \sin(\theta) ), where ( \theta ) is the angle between two adjacent sides.

For each triangular face, the area can be calculated using the formula for the area of a triangle: ( A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} ).

The height of the triangular faces can be found using trigonometric relationships within the pyramid. Since the height of the pyramid is 2 and the base angles of the rhombus are ( \frac{\pi}{6} ) and ( \frac{5\pi}{6} ), the height of each triangular face can be calculated using trigonometric functions.

After finding the areas of the base and the four triangular faces, add them together to obtain 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.

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