# The base of a triangular pyramid is a triangle with corners at #(6 ,7 )#, #(2 ,5 )#, and #(3 ,1 )#. If the pyramid has a height of #5 #, what is the pyramid's volume?

Volume of pyramid

Volume of pyramid

Where

Using shoelace formula,

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

To find the volume of a triangular pyramid, you can use the formula:

[ V = \frac{1}{3} \times \text{base area} \times \text{height} ]

Given:

- Base of the triangular pyramid with vertices at ( (6, 7) ), ( (2, 5) ), and ( (3, 1) ).
- Height of the pyramid is ( h = 5 ).

First, calculate the area of the base triangle using the coordinates provided and the formula for the area of a triangle given its vertices.

Then, substitute the calculated base area and the given height into the formula for the volume of a pyramid.

Calculate the volume using these values.

Alternatively, you can use the method of vectors to find the area of the base triangle and then proceed with the volume calculation as described above.

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.

- An ellipsoid has radii with lengths of #6 #, #5 #, and #9 #. 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?
- A cone has a height of #16 cm# and its base has a radius of #5 cm#. If the cone is horizontally cut into two segments #12 cm# from the base, what would the surface area of the bottom segment be?
- A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #2 # and #9 # 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?
- The base of a triangular pyramid is a triangle with corners at #(7 ,6 )#, #(4 ,3 )#, and #(1 ,8 )#. If the pyramid has a height of #6 #, what is the pyramid's volume?
- The base of a triangular pyramid is a triangle with corners at #(3 ,8 )#, #(4 ,2 )#, and #(9 ,8 )#. If the pyramid has a height of #4 #, what is the pyramid's volume?

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