The base of a triangular pyramid is a triangle with corners at (3 ,8 )(3,8), (4 ,1 )(4,1), and (9 ,8 )(9,8). If the pyramid has a height of 4 4, what is the pyramid's volume?
1 Answer
Jun 21, 2018
Explanation:
"the volume (V) of a pyramid is calculated using"the volume (V) of a pyramid is calculated using
•color(white)(x)V=1/3xx"area of base"xx"height"∙xV=13×area of base×height
"the area (A) of the triangular base is calculated using"the area (A) of the triangular base 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)|∙xA=12|x1(y2−y3)+x2(y3−y1)+x3(y1−y2)|
"let "(x_1,y_1)=(3,8),(x_2,y_2)=(4,1),(x_3,y_3)=(9,8)let (x1,y1)=(3,8),(x2,y2)=(4,1),(x3,y3)=(9,8)
A=1/2|3(1-8)+4(8-8)+9(8-1)|A=12|3(1−8)+4(8−8)+9(8−1)|
color(white)(A)=1/2|-21+0+72|=51/2A=12|−21+0+72|=512
V=1/3xx51/2xx4=34" units"^3V=13×512×4=34 units3
