The base of a triangular pyramid is a triangle with corners at (2 ,5 ), (6 ,4 ), and (7 ,8 ). If the pyramid has a height of 4 , what is the pyramid's volume?

1 Answer
Jim G.
Jan 31, 2018

"volume "=34/3

Explanation:

"the volume (V) of a pyramid is calculated using"

•color(white)(x)V=1/3xx"area of base "xx"height"

"the area (A) of the triangle can be found using"

A=1/2|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|

"let "(x_1,y_1)=(2,5),(x_2,y_2)=(6,4),(x_3,y_3)=(7,8)

A=1/2|2(4-8)+6(8-5)+7(5-4)|

color(white)(A)=1/2|-8+18+7|=17/2

rArrV=1/3xx17/2xx4=34/3" cubic units"

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