The base of a triangular pyramid is a triangle with corners at (1 ,3 )(1,3), (2 ,2 )(2,2), and (8 ,5 )(8,5). If the pyramid has a height of 7 7, what is the pyramid's volume?

1 Answer
Sep 12, 2017

Volume of pyramid is 10.5 10.5 cu.unit.

Explanation:

x_1=1 ,y_1=3 ,x_2=2 ,y_2=2,x_3=8 ,y_3=5x1=1,y1=3,x2=2,y2=2,x3=8,y3=5

Area of Triangle A_t= 1/2(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))At=12(x1(y2y3)+x2(y3y1)+x3(y1y2)) or

A_t= 1/2(1(2−5)+2(5−3)+8(3−2))At=12(1(25)+2(53)+8(32)) or

A_t= 1/2(-3+4+8)= 9/2 =4.5 At=12(3+4+8)=92=4.5 sq.unit

Volume of pyramid is V_p=1/3*A_b*h ;Vp=13Abh; where base area

is A_b = A_t= 4.5 , h=7Ab=At=4.5,h=7( hight).

:.V_p=1/3*4.5*7 = 10.5 cu.unit.

Volume of pyramid is 10.5 cu.unit. [Ans]