# The base of a triangular pyramid is a triangle with corners at #(6 ,3 )#, #(4 ,7 )#, and #(8 ,8 )#. If the pyramid has a height of #6 #, what is the pyramid's volume?

Volume of pyramid

Three vertices' coordinates are A (6,3), B (4,7), and C (8,8). The pyramid's height is equal to 6.

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

To find the volume of the triangular pyramid, we first need to calculate the area of the base triangle and then use the formula for the volume of a pyramid, which is one-third of the product of the base area and the height.

Given the coordinates of the three vertices of the base triangle: (6, 3), (4, 7), and (8, 8), we can use the formula for the area of a triangle formed by three points in the coordinate plane.

The formula for the area of a triangle formed by three points (x1, y1), (x2, y2), and (x3, y3) is:

[ Area = \frac{1}{2} |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)| ]

After calculating the area of the base triangle, we can use the formula for the volume of the pyramid:

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

Substitute the calculated area of the base triangle and the given height (6) into this formula to find 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 radius of a circle inscribed in an equilateral triangle is 2. What is the perimeter of the triangle?
- Box 1 has dimensions 6/1/2 by 8/1/2 by 11. Box 2 has dimensions 3/3/8 by 11/7/8 by 13/5/8. Which box has the greater volume?
- A triangle has two corners with angles of # (2 pi ) / 3 # and # ( pi )/ 4 #. If one side of the triangle has a length of #2 #, what is the largest possible area of the triangle?
- What is the volume of a rectangular based cone?
- A triangle has two corners with angles of # pi / 12 # and # pi / 3 #. If one side of the triangle has a length of #14 #, what is the largest possible area of the triangle?

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