# The base of a triangular pyramid is a triangle with corners at #(3 ,1 )#, #(4 ,9 )#, and #(5 ,7 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?

Hero's recipe:

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

To find the volume of the triangular pyramid, we can use the formula for the volume of a pyramid, which is one-third of the product of the base area and the height.

First, we need to find the area of the triangular base. We can use the formula for the area of a triangle given its coordinates.

Let the coordinates of the vertices of the triangle be ( (x_1, y_1), (x_2, y_2), (x_3, y_3) ). Then, the area of the triangle is given by:

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

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

After finding the area of the base, which is the triangle, we multiply it by the height of the pyramid and then divide by 3 to get the volume of the pyramid.

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.

- The base of a triangular pyramid is a triangle with corners at #(5 ,1 )#, #(2 ,3 )#, and #(9 ,4 )#. If the pyramid has a height of #4 #, what is the pyramid's volume?
- How do you find the area of a parallelogram with base b = 87 cm and height h = 18.6 cm?
- Two corners of an isosceles triangle are at #(1 ,5 )# and #(6 ,7 )#. If the triangle's area is #4 #, what are the lengths of the triangle's sides?
- 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 #33 # and the height of the cylinder is #13 #. If the volume of the solid is #232 pi#, what is the area of the base of the cylinder?
- The base of a triangular pyramid is a triangle with corners at #(3 ,4 )#, #(6 ,2 )#, and #(5 ,5 )#. If the pyramid has a height of #7 #, 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