# Parallelograms on the Same Base and between the Same Parallels

## Trending Questions

**Q.**

Prove that if the diagonals of a parallelogram are perpendicular, then it is a rhombus. [3 MARKS]

**Q.**

Two parallelograms are on the same base and between the same parallels. The ratio of their areas is

1:2

3:1

2:1

1:1

**Q.**

If ${p}_{1},{p}_{2},{p}_{3}$ are respectively the perpendiculars from the vertices of a triangle to the opposite side, then ${p}_{1}{p}_{2}{p}_{3}$ is equal to

${a}^{2}{b}^{2}{c}^{2}$

$2{a}^{2}{b}^{2}{c}^{2}$

$\frac{4{a}^{2}{b}^{2}{c}^{3}}{{R}^{2}}$

$\frac{{a}^{2}{b}^{2}{c}^{2}}{8{R}^{3}}$

**Q.**Question 9

If a triangle and a parallelogram are on the same base and between same parallels, then the ratio of the area of the triangle to the area of the parallelogram is:

A) 1:3

B) 1:2

C) 3:1

D) 1:4

**Q.**

If parallelogram ABCD and rectangle ABEM are of equal area, then:

Perimeter of AMEB = 12 Perimeter of ADCB

Perimeter of AMEB < Perimeter of ADCB

Perimeter of AMEB = Perimeter of ADCB

Perimeter of AMEB >Perimeter of ADCB

**Q.**

Two parallel sides of trapezium are 12 cm and 8 cm long and the distance between them is 6.5 cm.The area of the trapezium is

(a) 74 cm2

(b) 32.5 cm2

(c) 65 cm2

(d) 130 cm2

**Q.**Two triangles have the same base and equal areas have their vertex lying on the same side of their base. The line joining the two apexes will be _______ to their base.

- double
- equal
- parallel
- intersecting

**Q.**

Question 1 (d)

Find the area of each of the following parallelograms:

**Q.**

A parallelogram and rectangle are on the same base and between the same parallel lines. Then perimeter of rectangle is:

less than the perimeter of the parallelogram.

equal to the perimeter of the parallelogram.

greater than the perimeter of the parallelogram.

Twice the perimeter of the parallelogram.

**Q.**

The base and height of a parallelogram are 4 cm and 6 cm respectively. Find the area of the parallelogram

**Q.**

Which of the following figures, you find polygons on the same base and between the same parallels?

**Q.**The parallel sides of a trapezoid ABCD are 3 cm and 9 cm. The non-parallel sides are 4 cm and 6 cm. A line EF parallel to the bases divides the trapezoid into two trapezoids of equal perimeters. What is the ratio in which each of the non-parallel sides is divided?

- 4:3
- 3:2
- 4:1
- 3:1

**Q.**Question 7

Two parallelograms are on equal bases and between the same parallels the ratio of their areas is:

A) 1:2

B) 1:1

C) 2:1

D) 3:1

**Q.**

In the figure, ABCD is a rectangle with sides AB = 10 cm and AD = 5 cm. Find the area of △EFG.

**Q.**Parallelogram PQRS, ΔPQS and rectangle PQTU have the same base PQ. If the area of ΔPQS=48 cm2, then find the area of rectangle PQTU.

- 96 cm2
- 48 cm2
- 100 cm2
- 50 cm2

**Q.**

ABCD is a parallelogram. E is a point on BA such That BE = 2 EA and F is a point on DC such that DF = 2FC. Prove that AECF is a parallelogram whose area is one third of the area of paralllelogram ABCD.

**Q.**

In the given figure, ABCD and ABFE are parallelograms scuh that ar(quad.EABC)=17 cm2 and ar(||gm ABCD)=25 cm2.Then, ar(△ BCF)=?

(a) 4 cm2

(b) 4.8 cm2

(c) 6 cm2

(d) 8 cm2

**Q.**Question 5 (i)

Inthe given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that:

(i) ar (PQRS) = ar (ABRS)

**Q.**In ΔABC, AB=16cm, BC=9.6cm.CD⊥AB and AE⊥BC. If CD = 6 cm, the find the length of AE.

**Q.**Question 8

XY is a line parallel to side BC of a triangle ABC. If BE || AC and CF || AB meet XY at E and F respectively,

show that ar(ΔABE)=ar(ΔACF).

**Q.**

**Question 8**

XY is a line parallel to side BC of a triangle ABC. If BE || AC and CF || AB meet XY at E and F respectively,

show that ar(ΔABE)=ar(ΔACF).

**Q.**In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that .

ar(ΔAXS)=12ar(PQRS)

**Q.**

Prove that in a regular pentagon, the perpendicular from any vertex to the opposite side bisects that side.

**Q.**Question 2

Write True or False and justify your answer:

The area of a ΔABC is 8 cm2 in which AB = AC = 4 cm and ∠A=90∘

**Q.**Question 4

In the following figure, ABCD is a parallelogram and BC is produced to a point Q such that AD =CQ. If AQ intersects DC at P,

Show that ar (BPC) = ar (DPQ).

**Q.**A rectangle and a square have the same base and are between the same parallels. The ratio of their areas

- 1 : 2
- 1 : 4
- 1 : 1
- 2 : 1

**Q.**ABCD is a parallelogram, E and F are the midpoints of AB and CD respectively then the ratio of areas of AEFD and EBCF is ______ .

- 1:3
- 1:1
- 1:2
- 2:1

**Q.**

In the given figure ABCD is a parallelogram. If area of parallelogram ABCD = 708 square units, then what is the area of ΔBEC?

**Q.**

Look at the statemets given below:

I.A parallelogram and a rectangle on the same base and between the same parallels are equal area.

II.In a ||gm ABCD, it is given that AB=10 cm.The altitudes DE on AB and BF on AD being 6 cm and 8 cm respectively, then AD=7.5 cm.

III.Area of a ||gm=12×base×altitude.

Which is true?

(a) I only

(b) II only

(c) I and II

(d) II and III

**Q.**

In a parallelogram ABCD, AB=10 cm. The altitudes corresponding to the sides AB and AD are respectively 7 cm and 8 cm. Find AD.