Question

Please help i don't know the answer to number 11

Answer 1

The length of midpoint connected size is half of the size of the triangle that it's parallel to. that's means lengh of sizes are half of the original.

area of triangle with known side a, b, c
s = (a+b+c)/2
area = sqrt(s(s-a)(s-b)(s-c))

area of midpoint triangle wih side a/2, b/2, c/2
s' = (a/2+b/2+c/2)/2 = (a+b+c)/4 = s/4
area' = sqrt(s'(s'-a/2)(s'-b/2)(s'-c/2))
= sqrt(s/2(s/2-a/2)(s/2-b/2)(s/2-c/2))
= (1/4)sqrt(s(s-a)(s-b)(s-c)) = (1/4)area

answer is 1/4