Volume of a pyramid is given by 1/3xx"area of base"xxheight13×area of base×height
Hence, we have to first find area of base triangle and as all the three sides can be found between three points, we would be using Heron's formula i.e. area of triangle is given by sqrt(sxx(c-a)(s-b)(s-c))√s×(c−a)(s−b)(s−c), where s=1/2(a+b+c)s=12(a+b+c).
Let the points be A(7,6)A(7,6), B(4,2)B(4,2) and C(3,8)C(3,8). Hence
a=sqrt((3-4)^2+(8-2)^2)=sqrt((-1)^2+6^2)=sqrt(1+36)=sqrt37=6.083a=√(3−4)2+(8−2)2=√(−1)2+62=√1+36=√37=6.083
b=sqrt((3-7)^2+(8-6)^2)=sqrt((-4)^2+2^2)=sqrt(16+4)=sqrt20=4.472b=√(3−7)2+(8−6)2=√(−4)2+22=√16+4=√20=4.472
c=sqrt((7-4)^2+(6-2)^2)=sqrt(3^2+4^2)=sqrt(9+16)=sqrt25=5c=√(7−4)2+(6−2)2=√32+42=√9+16=√25=5
Hence s=1/2(6.083+4.472+5)=15.555/2=7.777s=12(6.083+4.472+5)=15.5552=7.777 and
Area of triangle is sqrt(7.777(7.777-6.083)(7.777-4.472)(7.777-5)√7.777(7.777−6.083)(7.777−4.472)(7.777−5) or
sqrt(7.777xx1.694xx3.305xx2.777)=sqrt120.913=10.996√7.777×1.694×3.305×2.777=√120.913=10.996
Hence volume of pyramid is 1/3xx10.996xx6=2xx10.996=21.99213×10.996×6=2×10.996=21.992