Question

if {1,2} {3,4} and {5,7} are the mid points of the sides of a triangle, then the area of the triangle is

Answer 1

Area of the triangle = 4 × Area of the triangle formed by joining the midpoints

of the sides

The formula to calculate the area of the triangle is:

\frac{1}{2} [x_{1} (y_{2} - y_{3})+x_{2} (y_{3} - y_{1})+x_{3} (y_{1} - y_{2})}]

So, area of the triangle formed by joining the midpoints of the sides of the given triangle is:

\frac{1}{2} [1 (4 - 7)+3 (7 - 2)+5 (2 - 4)}]

= \frac{1}{2} [(- 3)+15+(- 10)}]

= \frac{1}{2} (2)=

2

1

(2)

= 1 square unit

Hence, area of the given triangle = 4 × 1 = 4 square units.

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