Question

If ABCD is a parallelogram, then prove that

ar (ΔABD) = ar (ΔBCD) = ar (ΔABC) = ar (ΔACD) = $\frac{1}{2}$ ar (||^gm ABCD)

Answer 1

Given: Here in the question it is given that

(1) ABCD is a Parallelogram

To Prove :

(1)

(2)

(3)

(4)

Construction: Draw

Calculation: We know that formula for calculating the

Area of Parallelogram = base × height

Area of paralleogram ABCD = BC × AE (Taking base as BC and Height as AE ……(1)

We know that formula for calculating the

Area of ΔADC = Base × Height

(AD is the base of ΔADC and AE is the height of ΔADC)

= Area of Parallelogram ABCD (from equation1)

Hence we get the result

Similarly we can show that

(2)

(3)

(4)