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

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)\\\\ </p><p></p><p> \because\: Ar(\parallel^(gm) ABEF) \\=Ar(\triangle AFD) + Ar(\square \: ABED)....(2) \\\\</p><p></p><p>\&\: 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) </p><p> \\ \\ \purple {\boxed {\therefore Ar(\triangle AFD) = Ar(\triangle BCE)}} </p><p> \\`

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

Hence proved.