Question

A farmer has two pieces of land in a parallelogram shape on the same base. He grows vegetables and flowers in two triangular pieces of land as shown in diagram.
Q: Check whether the two triangular pieces of land are equal in area.​

Answer 1

Step-by-step explanation:

In trapezoid ABCF, AB || CF.

Therefore, parallelograms ABEF & ABCD have same height and lie on the same base AB.

$\therefore Ar(\parallel^{gm} ABEF) = Ar(\parallel^{gm}ABCD)\\... (1)\\\\ \because\: Ar(\parallel^{gm} ABEF) \\=Ar(\triangle AFD) + Ar(\square \: ABED)....(2) \\\\\&\: Ar(\parallel^{gm}ABCD)\\= Ar(\triangle BCE) +Ar(\square ABED)....(3)$

From equations (1), (2) & (3), we find:

$Ar(\triangle AFD) + Ar(\square \: ABED) \\ = Ar(\triangle BCE) +Ar(\square ABED) \\ \\ \purple {\boxed {\therefore Ar(\triangle AFD) = Ar(\triangle BCE)}}$

Thus, the two triangular pieces of land are equal in area.

Hence proved.