# 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 #3 #, its base has sides of length #6 #, and its base has a corner with an angle of # pi/3 #. What is the pyramid's surface area?

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

The surface area ( A ) of a pyramid with a rhombus base can be calculated using the formula:

[ A = \text{Area of Base} + \text{Area of Each Triangle Face} \times 4 ]

For a rhombus with side length ( s ) and an angle ( \theta ) between adjacent sides, the area is ( A_{\text{rhombus}} = s^2 \sin(\theta) ).

Given that the side length of the rhombus base is ( 6 ) and one angle is ( \frac{\pi}{3} ), the area of the base is:

[ A_{\text{base}} = 6^2 \sin\left(\frac{\pi}{3}\right) ]

The height of the pyramid is ( 3 ), so the area of each triangular face is:

[ A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 3 ]

Thus, the total surface area of the pyramid is:

[ A = A_{\text{base}} + A_{\text{triangle}} \times 4 ]

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

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.

- 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 #8 #, its base has sides of length #5 #, and its base has a corner with an angle of #(3 pi)/4 #. What is the pyramid's surface area?
- An ellipsoid has radii with lengths of #8 #, #9 #, and #5 #. A portion the size of a hemisphere with a radius of #5 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?
- Sarah is painting a box to use as a prop in her dance routine. If the box is 18 inches long, 16 inches wide, and 12 inches tall, what is the surface area of the box to be painted?
- What is the volume of a cube with a side length if 2.1 centimeters?
- An ellipsoid has radii with lengths of #6 #, #5 #, and #3 #. A portion the size of a hemisphere with a radius of #6 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7