# The base of a triangular pyramid is a triangle with corners at #(6 ,7 )#, #(4 ,5 )#, and #(8 ,7 )#. If the pyramid has a height of #6 #, what is the pyramid's volume?

Then a pyramid's volume is:

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} ]

First, calculate the area of the base triangle using the coordinates given for its vertices. You can use the formula for the area of a triangle given its coordinates:

[ \text{Area} = \frac{1}{2} \times |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| ]

Substitute the given coordinates into the formula to find the area of the base triangle.

Next, multiply the area of the base triangle by the height of the pyramid.

[ V = \frac{1}{3} \times \text{Area of Base} \times \text{Height} ]

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.

- Prove that the purple shaded area is equal to the area of incircle of the equilateral triangle (yellow striped circle)?
- How do you find the circumference of a circle with a radius of 0.5 meters?
- A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #12 # and the height of the cylinder is #4 #. If the volume of the solid is #16 pi#, what is the area of the base of the cylinder?
- A triangle has two corners with angles of # pi / 2 # and # (3 pi )/ 8 #. If one side of the triangle has a length of #12 #, what is the largest possible area of the triangle?
- An ellipsoid has radii with lengths of #14 #, #4 #, and #6 #. A portion the size of a hemisphere with a radius of #2 # 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