# Triangle and Parallelogram of Same Base and Between the Same Parallels

#### Summary

The parallelograms are on the same base and between the same parallels.

Area of a Parallelogram = b × h

In both parallelograms:

• The bases are equal.

• The heights are equal.

Area of parallelogram ABCD = Area of parallelogram ABGH.

Parallelograms on the same base and between the same parallels are equal in area.

**Theorem:**

Prove that the area of the triangle is equal to half the area of the parallelogram, if they are on the same base and are between the same parallels.

Given:

Δ ABP and parallelogram ABCD are on same base AB and between the same parallels AB and PC.

To Prove: ar (ΔABP) =1/2 ar ( ||gm ABCD)

Construction: Draw BQ || AP

Proof:

ar ( ||gm ABQP) = ar ( || gm ABCD (Parallelograms on the same base and between the same parallels are equal in area.)

Δ ABP ≅ Δ BQP

ar (Δ ABP) = ar (Δ BQP)

ar (Δ ABP) = (½) ar (|| gm ABQP)

ar (Δ ABP) = (½) ar (|| gm ABCD).

#### Questions & Answers*arrow_upward*

### 1 . Three squares are joined at there corners and strung between two vertical poles as shown. Find the value of x.

Recall that sum of angles of a polygon = (2n - 4) × 90°

Here number of sides, n = 9

Hence the sum of angles of the given pol...

### 2 . An open tin box,21 cm long,9 cm wide,8 cm high,is fitted with a tin lid which overlaps to a depth of 1 cm alll round.What is the total area of tin sheeting used for the box and the lid??

Length = 21 cm

Breadth = 9 cm

width = 8 cm

Surface Area of tin box (excluding lid)

= 2(bh+hl) + lb...

### 3 . formula for area of equilateral triangle

root3/4 a suare

### 4 . Find the height of the parallelogram.

Sol:

Perimeter of triangle = ( a + b + c) = (26 + 28 + 30) cm = 84 cm

2
*s* = 84 cm

*s* = 42 cm,a =...

### 5 . find the area of figure.All corners are right angles.AB= 4 [int]1/4,BC=2[int]3/4,DE=3[int]1/2,EF=4,FG=4[int]1/2...

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