Question

A point p lies on the side CD of parallelogram ABCD . If ar (abcd) =56cm2 then ar (pab) = cm2

Answer 1

Answer:

KATTAR MIYA BHAE RAIIN HAI

Answer 2

Answer: 28 cm²

Step by step explanation :-

Given area of the Parallelogram = 56 cm²

P is a point on the side of CD, now its not mentioned where P lies so you can assume it to be the mid-point of CD (For easier explanation).

Now,

Since the bases of ΔBPC and ΔAPD are equal with their the same height (in between two ║ lines)

area of ΔBPC = area of ΔAPD ---- eq. 1

Now draw a line through P parallel to BC and bisecting AB at point H,

through this we can prove that ΔHAP ≅ ΔPDA.

Now we know that area of parallelogram HPDA = 28 cm²

So, area of ΔPDA = 14 cm² ----- eq. 2

From eq. 1 and eq. 2,

area of ΔPDA + ΔBPC = 28 cm²

and area of ΔPAB = area of parallelogram ABCD - (area of ΔPDA + ΔBPC)

⇒ area of ΔPAB = 28 cm²

Note :- This answer also proves that the area of the triangle made with one of the sides of the parallelogram as the base and the third vertex on the opposite side of the parallelogram is half the area of the parallelogram.