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 #2 #. If one of the base's corners has an angle of #(5pi)/6#, what is the pyramid's surface area?
T S A = 7.4788
Lateral surface area = Total surface area =Area of parallelogram base + Lateral surface area
Area of parallelogram base
Area of
Area of
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The surface area of the pyramid can be calculated using the formula:
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
Given that the base is a parallelogram with side lengths of 2 and 1, and one of the base's corners has an angle of (5π)/6, the base area can be calculated as the product of the base's side lengths times the sine of the given angle.
Base Area = (2 * 1) * sin((5π)/6)
The perimeter of the base can be calculated by summing the lengths of the sides.
Perimeter of Base = 2 + 2 + 1 + 1 = 6
The slant height of the pyramid can be found using the Pythagorean theorem, considering that the slant height is the hypotenuse of a right triangle formed by the height of the pyramid and half of the diagonal of the base.
Slant Height = √(2^2 + (1/2)^2) = √(4 + 1/4) = √(17/4)
Now, plug the values into the formula for the surface area:
Surface Area = (2 * 1) * sin((5π)/6) + (1/2) * 6 * √(17/4)
Calculate the values and you'll get the 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.
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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