A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is #2 #, its base has sides of length #7 #, and its base has a corner with an angle of #(3 pi)/4 #. What is the pyramid's surface area?
T S A = 91.0838
AB = BC = CD = DA = a = 7
Height OE = h = 2
OF = a/2 = 7/2 = 3.5
Area of
Lateral surface area
Area of base ABCD
T S A
T S A
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To find the surface area of the pyramid, calculate the area of the base and then add the areas of the four triangular faces.

Area of the base (rhombus): A = (d₁ * d₂) / 2, where d₁ and d₂ are the diagonals of the rhombus. Given that the sides of the base are 7 units and the angle between them is ( \frac{3\pi}{4} ) radians, you can find the diagonals using the cosine rule: ( d = \sqrt{a^2 + b^2  2ab \cos(\theta)} ), where ( a ) and ( b ) are the side lengths and ( \theta ) is the angle between them.

Once you have the diagonals, calculate the area of the base using the formula ( A = (d₁ * d₂) / 2 ).

Calculate the area of each triangular face using the formula ( A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} ). The height of each triangular face is the pyramid's height, which is given as 2 units.

Add the areas of the base and the four triangular faces to get the total surface area of the pyramid.
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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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