Question

4) The given figure shows ∆ABC. Points D,E and F are the mid-points of sides AB,AC and BC respectively. Sides AB, BC and CA measure 6 cm, 10 cm and 8 cm respectively. What is the area of ∆DEF? *

Answer 1

the area of ∆DEF = 6 cm²

Explanation:

The midpoint theorem states that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

DE // BC and DE = BC/2 = 10/2 = 5

same reason: DF = AC/2 = 4

FE = AB/2 = 3

DF² + FE² = 16 + 9 = 25 = 5² = DE²

by the Pythagorean theorem, ΔDFE is a right triangle

area ΔDEF = (3 x 4) / 2 = 6 cm²