A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #3 # and #7 # and the pyramid's height is #8 #. If one of the base's corners has an angle of #(3pi)/8#, what is the pyramid's surface area?
Short sides:
Long sides:
Thus the total surface area of the pyramid:
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To find the surface area of the pyramid, you first need to calculate the area of the base and then add the areas of the four triangular faces.

Area of the base (parallelogram): Area = base × height Area = 7 × 3 = 21 square units

To find the area of each triangular face, you'll need to calculate the base and height of each triangle. The base is the side length of the base of the pyramid (either 3 or 7), and the height is the slant height of the pyramid, which can be found using the Pythagorean theorem.

Calculate the slant height (l) of the pyramid: l = √(h^2 + (b/2)^2) l = √(8^2 + (3/2)^2) [Since the base is a parallelogram, the diagonal length is used as the height (h)] l ≈ √(64 + 2.25) l ≈ √66

Calculate the area of one triangular face: Area = 0.5 × base × height Area = 0.5 × 3 × √66

Calculate the area of all four triangular faces and add them together: Total triangular area = 4 × (0.5 × 3 × √66)

Finally, add the base area and the total triangular area to find the total surface area of the pyramid: Surface area = Base area + Total triangular area
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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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