# 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

Area of parallelogram base

Area of

Area of

Lateral surface area =

Total surface area =Area of parallelogram base + Lateral surface area

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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.

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- A rectangular box has the dimensions #12\times 18 \times 14# inches. What's its volume? What's its surface area?
- A chord with a length of #5 # runs from #pi/8 # to #pi/2 # radians on a circle. What is the area of the circle?
- Two corners of a triangle have angles of # (3 pi )/ 8 # and # ( pi ) / 2 #. If one side of the triangle has a length of # 7 #, what is the longest possible perimeter of the triangle?

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