A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #6 # and #4 # and the pyramid's height is #3 #. If one of the base's corners has an angle of #pi/4#, what is the pyramid's surface area?
The pyramid's semidiagonal base is shaped like a parallelogram.
The sides of the pyramid's triangular lateral face are now listed as
And now, the area of the pyramid's lateral triangular face using Heron's formula
And now, the area of the pyramid's lateral triangular face using Heron's formula
Therefore, the pyramid's total surface area (including the base area)
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The surface area of the pyramid can be calculated by finding the areas of its different faces and then summing them up.

The area of the base (a parallelogram) can be calculated using the formula for the area of a parallelogram: ( \text{Area}_{\text{base}} = \text{base} \times \text{height} = 6 \times 4 ).

The area of each triangular face can be calculated using the formula for the area of a triangle: ( \text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} ). Since the height of the pyramid is given as 3, and the length of the base of the triangle is half of the corresponding side of the base parallelogram, the lengths of the base and height of each triangular face can be determined using trigonometric relations.

There are four triangular faces in total.

The area of each triangular face with the base's corner angle of ( \frac{\pi}{4} ) can be calculated using trigonometric relations.

Sum up the areas of the base and the triangular faces to find the total surface area of the pyramid.
By following these steps, the surface area of the pyramid can be determined.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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