The base of a triangular pyramid is a triangle with corners at (1 ,2 ), (9 ,5 ), and (4 ,7 ). If the pyramid has a height of 9 , what is the pyramid's volume?

2 Answers
Apr 1, 2018

Volume of a pyramid is 46.5 cubic.unit.

Explanation:

Volume of a pyramid is 1/3*base area *hight.

(x_1,y_1)=(1 ,2) ,(x_2,y_2)=(9,5),(x_3,y_3)=(4,7) , h=9

Area of Triangle is A_b = |1/2(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))|

A_b = |1/2(1(5−7)+9(7−2)+4(2−5))| or

A_b = |1/2(-2+45-12)| = | 31/2| =31/2sq.unit

Volume of a pyramid is 1/3*A_b*h = 1/3 *31/2*9 = 46.5

cubic.unit [Ans]

Apr 1, 2018

"volume "=93/2

Explanation:

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

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

"the area of the base (A) is calculated using"

•color(white)(x)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)=(1,2),(x_2,y_2)=(9,5),(x_3,y_3)=(4,7)

A=1/2|1(5-7)+9(7-2)+4(2-5)|

color(white)(A)=1/2|-2+45-12|=31/2

rArrV=1/3xx31/2xx9=93/2