Question

AREAS OF PARALLELOGRAMS AND TRIANGLES
Prove that the median of a triangle divides it into two triangles of equal areas. Hence, find ar(ABD) if ar(ABC) = 30 cm2, where AD is the median.

Answer 1

refer to the attachment

Answer 2

Step-by-step explanation:

1st Part:

The 2 attached images have your proof.

2nd Part:

ar(ΔABC) = 30 $cm^{2}$

ar(ΔABD) + ar(ΔADC) = 30 $cm^{2}$

2 × ar(ΔABD) = 30 $cm^{2}$                 [ar(ΔABD) = ar(ΔADC)]

ar(ΔABD) = 15 $cm^{2}$