A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #4 # and #5 # and the pyramid's height is #4 #. If one of the base's corners has an angle of #pi/3#, what is the pyramid's surface area?
T S A = 58.5491
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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To find the surface area of the pyramid, we need to calculate the area of the base and the area of the four triangular faces.

Area of the base: Since the base is a parallelogram, its area is given by the formula for the area of a parallelogram: base multiplied by height. Given that the base has sides of length 4 and 5, and the height of the parallelogram is 4, the area of the base is ( 4 \times 5 = 20 ) square units.

Area of the triangular faces: Each triangular face is a right triangle, with one leg being the height of the pyramid (given as 4 units) and the other leg being the slant height of the pyramid. We can find the slant height using trigonometry since we know one angle of the base triangle is ( \pi/3 ) and the adjacent side is 5 (one of the sides of the base).
Using trigonometry, the slant height, denoted as ( l ), is ( l = 5 \sin(\pi/3) = 5 \times \sqrt{3}/2 = (5 \sqrt{3})/2 ) units.
Now, the area of each triangular face is ( \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times \frac{5 \sqrt{3}}{2} = 5 \sqrt{3} ) square units.

Total surface area: The total surface area of the pyramid is the sum of the area of the base and the four triangular faces. Therefore, the total surface area is ( 20 + 4 \times (5 \sqrt{3}) = 20 + 20 \sqrt{3} ) square units.
So, the surface area of the pyramid is ( 20 + 20 \sqrt{3} ) square units.
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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.
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