Question 25.

It is given that AD and BE are medians which are perpendicular to each other.

The lengths of AD and BE are 12cm and 9cm respectively.

It is known that the centroid G divides the median in the ratio of 2:1

Area of $\triangle$ ABC = 2* Area of the triangle ABD

Area of $\triangle$ABD = Area of $\triangle$ AGB + Area of $\triangle$ BGD

Since $\angle AGB = \angle BGD = 90$ (Given)

Area of $\triangle$ AGB = $\frac{1}{2}\times 8 \times 6$ = 24

Area of $\triangle$ BGD = $\frac{1}{2}\times 6 \times 4$ = 12

Area of $\triangle$ABD = 24+12=36

Area of $\triangle ABC =2\times 36=72$