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?

Answer 1

T S A = 91.0838

AB = BC = CD = DA = a = 7
Height OE = h = 2
OF = a/2 = 7/2 = 3.5
# EF = sqrt(EO^2+ OF^2) = sqrt (h^2 + (a/2)^2) = sqrt(2^2+3.5^2) = color(red)(4.0311)#

Area of #DCE = (1/2)*a*EF = (1/2)*7*4.0311 = color(red)(14.1089)#
Lateral surface area #= 4*Delta DCE = 4*14.1089 = color(blue)(56.4356)#

#/_C = (pi) - ((3pi)/4) = (pi)/4#
Area of base ABCD #= a* a * sin /_C = 7^2 sin (pi/4) = 34.6482#

T S A #= Lateral surface area + Base area#
T S A # =56.4356 + 34.6482 = color(purple)(91.0838)#

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the surface area of the pyramid, calculate the area of the base and then add the areas of the four triangular faces.

  1. 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.

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

  3. 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.

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

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7