# The base of a triangular pyramid is a triangle with corners at (3 ,8 ), (1 ,6 ), and (2 ,8 ). If the pyramid has a height of 4 , what is the pyramid's volume?

Jun 9, 2018

$\setminus \frac{8}{3}$ units^2

#### Explanation:

The area of the base (triangle) can be worked out from the vertices, as

Area = $\left\{2 \cdot 2\right\} \left\{2\right\} = 2$

Therefore by using the formula

$V = \left\{A \cdot h\right\} \left\{3\right\}$ we get the volume as $\setminus \frac{2 \cdot 4}{3} = \setminus \frac{8}{3}$

Jun 10, 2018

color(blue)("Volume of a pyramid "V_p = 1/3*A_b*h=1/3 *1*4 = 4/3

#### Explanation:

$\text{Area of triangle knowing three vertices on the coordinate plane is given by }$

color(crimson)(A_b = |1/2(x_1(y_2−y_3)+x_2(y_3−y_1)+x_3(y_1−y_2))|

$\left({x}_{1} , {y}_{1}\right) = \left(3 , 8\right) , \left({x}_{2} , {y}_{2}\right) = \left(1 , 6\right) , \left({x}_{3} , {y}_{3}\right) = \left(2 , 8\right) , h = 4$

A_b = |1/2(3(6−8)+1(8−8)+2(8−6))| = 1

color(crimson)("Volume of a pyramid " V_p = 1/3* A_b * h

color(blue)("Volume of a pyramid "V_p = 1/3*A_b*h=1/3 *1*4 = 4/3