Parallelograms on the Same Base and between the Same Parallels

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. 1:2

2. 3:1

3. 2:1
   

4. 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

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

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

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

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

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:

1. Perimeter of AMEB = $\frac{1}{2}$ Perimeter of ADCB

2. Perimeter of AMEB $<$ Perimeter of ADCB

3. Perimeter of AMEB = Perimeter of ADCB

4. 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) $74c{m}^2$

(b) $32.5c{m}^2$

(c) $65c{m}^2$

(d) $130c{m}^2$

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.

1. double
2. equal
3. parallel
4. 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:

1. less than the perimeter of the parallelogram.

2. equal to the perimeter of the parallelogram.

3. greater than the perimeter of the parallelogram.

4. 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?

1. 4$:$3
2. 3$:$2
3. 4$:$1
4. 3$:$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, $\Delta \text{PQS}$ and rectangle PQTU have the same base PQ. If the area of $\Delta \text{PQS}=48c{m}^2$, then find the area of rectangle PQTU.

1. $96{\text{cm}}^2$
2. $48{\text{cm}}^2$
3. $100{\text{cm}}^2$
4. $50{\text{cm}}^2$

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)=$17c{m}^2$ and ar(||gm ABCD)=$25c{m}^2$.Then, ar($△BCF$)=?

(a) $4c{m}^2$

(b) $4.8c{m}^2$

(c) $6c{m}^2$

(d) $8c{m}^2$

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 $\Delta ABC,AB=16cm,BC=9.6cm.CD\perp AB$ and $AE\perp BC$. 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 $ar\left(\Delta ABE\right)=ar\left(\Delta ACF\right)$.

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 $ar\left(\Delta ABE\right)=ar\left(\Delta ACF\right)$.

Q. In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that .
$ar\left(\Delta AXS\right)=\frac{1}{2}ar\left(PQRS\right)$

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 $\Delta ABC$ is 8 $c{m}^2$ in which AB = AC = 4 cm and $\angle A={90}^{\circ }$

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. 1 : 2
2. 1 : 4
3. 1 : 1
4. 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. 1:3
2. 1:1
3. 1:2
4. 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 $\Delta BEC$?

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=$\frac{1}{2}\times base\times altitude$.

Which is true?

(a) I only

(b) II only

(c) I and II

(d) II and III

Q.

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