Question

(i) In a given figure, BE is a median of $△$ ABD. If the area of parallelogram ABCD is 24 cm${}^2.$ Then the area of $△$ BDE is:

(ii) In the above diagram if AD = 12 cm then find the value of AE.

Answer 1

(i)In a parallelogram, triangle between the same parallels and on the same base have area which is equal to the half of that of parallelogram.

So, area of $△$ ABD $=\frac{1}{2}\times$ area of ABCD

BE is a median

Area of $△BDE=\frac{1}{2}\times$ area of $△$ ABD (Median divides the triangle into 2 equal areas)

Therefore,

Area of $△BDE=\frac{1}{4}\times$ area of ABCD $=\frac{1}{4}\times 24=6{\text{cm}}^2$

(ii) As we know that BE is a median,

$\therefore AE=\frac{1}{2}\times AD$

$AE=\frac{1}{2}\times 12=6$ cm