A triangular pyramid has a volume of 350 cubic centimetres and a height of 10 cm. Find one possible set of dimensions of the base

Answer 1

V = Bh/3 = 1/3 the Base area times height

350 = 10B/3

10B = 1050

B = 105 cm^2

105 = hb/2

hb =210

an equilateral triangle has h=bsin60 = sqr3/2(b)

210 = b(sqr3/2)b = b^2(sqr3/2

b = sqr[210/sqr3/2]= sqr[420/sqr3]

= 2sqr[105/sqr3]= length of each of 3 sides of the Base

or if the base is a right isosceles triangle

then 105 = bh/2 = h^2/2

h^2 = 210

h = sqr210 = b

with two sides = sqr210 and the 3rd = hypotenuse

where hypotenuse squared = 2(210= 420

hypotenuse = sqr420 = 2sqr105 = 3rd side of the Base, 1st&2nd sides =sqr210