# The base of a triangular pyramid is a triangle with corners at #(2 ,6 )#, #(5 ,2 )#, and #(8 ,7 )#. If the pyramid has a height of #18 #, what is the pyramid's volume?

Volume of pyramid

To determine the sides of a triangle:

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

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

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

First, we need to find the area of the base triangle. We can do this using the formula for the area of a triangle given its vertices (x1, y1), (x2, y2), and (x3, y3):

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

Substituting the given coordinates of the vertices, we can calculate the area of the base triangle.

Then, we plug the base area and the height of the pyramid into the formula for volume to find the volume of the pyramid. Make sure to use the appropriate units for consistency.

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 cone has a height of #6 cm# and its base has a radius of #6 cm#. If the cone is horizontally cut into two segments #2 cm# from the base, what would the surface area of the bottom segment be?
- The lengths of the sides of a triangle are in the ratio 5 : 6 : 7. What is the length of the longest side if the perimeter is less than 54 cm?
- The base of a triangular pyramid is a triangle with corners at #(6 ,5 )#, #(7 ,1 )#, and #(4 ,7 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?
- How do you use Heron's formula to find the area of a triangle with sides of lengths #15 #, #16 #, and #12 #?
- A chord with a length of #4 # runs from #pi/3 # to #pi/2 # radians on a circle. What is the area of the circle?

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