The following diagram shows two parallelograms ABCD and BEFG. Prove that : Area of // gm ABCD = Area of // gm BEFG.

Given: ABCD and BEFG are two parallelograms. To prove: Area of // gm ABCD = Area of // gm BEFG Construction: Join AC and GE. Proof: We know that if two triangles have the same base and height, their areas will be equal. Since AG is a common base, Area (Δ ACG) = Area (Δ AEG) Adding Area (Δ ABG) on both sides, ⇒ ar.(Δ ABC) + ar.(Δ ABG) = ar.(Δ ABG) + ar.(Δ BGE) ⇒ ar.(Δ ABC) = ar.(Δ BGE) ...................(1) Since the area of a triangle is always half the area of a parallelogram when they share the same base and height, we can write: ar.(Δ ABC) = ar.(∥gm ABCD) ar.(Δ BGE) = ar.(∥gm BEFG) From equation (1), ⇒ ar.(∥gm ABCD) = ar.(∥gm BEFG) ⇒ ar.(∥gm ABCD) = ar.(∥gm BEFG) Hence, Area of // gm ABCD = Area of // gm BEFG.

Construct a rhombus ABCD in which AC = 5.6 cm and BD = 6.3 cm

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Construct a rectangle ABCD with diagonal AC = 6.6 cm, side BC = 5.2 cm and ∠B = 90°.

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In the parallelogram ABCD, the side AB is produced to the point X, so that BX = AB. The line DX cuts BC at E. Prove that
(i) DBXC is a parallelogram.
(ii) Area (△ AED) = 2 x area (△ CEX).

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Mathematics

The following diagram shows two parallelograms ABCD and BEFG.
Prove that :
Area of // gm ABCD = Area of // gm BEFG.

Theorems on Area

Related Questions

Construct a rhombus ABCD in which AC = 5.6 cm and BD = 6.3 cm

Construct a rectangle ABCD with diagonal AC = 6.6 cm, side BC = 5.2 cm and ∠B = 90°.

In the parallelogram ABCD, the side AB is produced to the point X, so that BX = AB. The line DX cuts BC at E. Prove that
(i) DBXC is a parallelogram.
(ii) Area (△ AED) = 2 x area (△ CEX).

Mathematics

The following diagram shows two parallelograms ABCD and BEFG.Prove that :Area of // gm ABCD = Area of // gm BEFG.

Theorems on Area

Related Questions

Construct a rhombus ABCD in which AC = 5.6 cm and BD = 6.3 cm

Construct a rectangle ABCD with diagonal AC = 6.6 cm, side BC = 5.2 cm and ∠B = 90°.

In the parallelogram ABCD, the side AB is produced to the point X, so that BX = AB. The line DX cuts BC at E. Prove that(i) DBXC is a parallelogram.(ii) Area (△ AED) = 2 x area (△ CEX).

The following diagram shows two parallelograms ABCD and BEFG.
Prove that :
Area of // gm ABCD = Area of // gm BEFG.

In the parallelogram ABCD, the side AB is produced to the point X, so that BX = AB. The line DX cuts BC at E. Prove that
(i) DBXC is a parallelogram.
(ii) Area (△ AED) = 2 x area (△ CEX).