Problema Solution
A rectangular parallipipped has the dimension 8cm, 10cm and 12 cm. If the midpoints of any three sides meeting at a common vertex are connected by lines, find the area of the triangle by the connecting lines.
Answer provided by our tutors
First we will find the lengths of the sides if the triangle using Pythagorean Theorem and them using Heron's formula we will find the area of the triangle.
Let A, B and C be the midpoints with common vertex.
Using Pythagorean Theorem we have:
AB = √(4^2 + 6^2) = 2√13
BC = √(5^2 + 6^2) = √61
AC = √(4^2 + 5^2) = √41
Using Herons formula for the area we have:
s = (1/2)(AB+BC+AC)
s = (1/2)(2√13 + √61 + √41)
s = 10.71
A =√s(s−AB)(s−BC)(s−AC)
A = √10.71(10.71−2√13)(10.71−√61)(10.71−√41)
A = 143 cm^2
The area of the triangle is 143 cm^2.