Area of Parallelogram

Q.

The height of a parallelogram is one third of its base. If the area of the parallelogram is $192c{m}^2$, find its height and base.

Q. Which of the following are true for a parallelogram?

1. Diagonals bisect each other
2. The diagonals of the parallelogram separate it into two congruent triangles.
3. The consecutive angles in a parallelogram are supplementary.
4. The opposite angles of a parallelogram are always supplementary.

Q. Two adjacent sides of a parallelogram are 24 cm and 18 cm. If the distance between the longer sides is 12 cm, then the distance between the shorter sides is

1. 18 cm
2. 9 cm
3. 15 cm
4. 16 cm

Q. The area of parallelogram ABCD is $84c{m}^2$. Calculate the height of parallelogram ABCD and ABEF if AB $=2.1cm.$

Q. Question 1
In the given figure, ABCD is parallelogram, $AE\perp DC$ and $CF\perp AD$. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

Q.

In the given figure, ABCD is parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 6 cm, AE = 8cm and CF = 12 cm, find AD.
[2 MARKS]

Q.

In the given figure, ABCD is a parallelogram. P and Q are midpoints of AB and AD respectively. If the area of parallelogram ABCD is $20c{m}^2$, then the area of $\Delta APQ$ is

1. $2.5c{m}^2$

2. $5c{m}^2$

3. $10c{m}^2$

4. $40c{m}^2$

Q. Area of a parallelogram = product of the lengths of its two adjacent sides.

1. False
2. True

Q. The bisectors of any two adjacent angles of a parallelogram intersect at

(a) 30°

(b) 45°

(c) 60°

(d) 90°

Q. Write the following statements in 'if-then' form.
(i) The opposite angles of a parallelogram are congruent.
(ii) The diagonals of a rectangle are congruent.
(iii) In an isosceles triangle, the segment joining the vertex and the mid point of the base is perpendicular to the base.

Q.

Which of the following is not true for a parallelogram?

1. Diagonals bisect each other

2. Opposite sides are equal

3. Opposite angles are bisected by diagonals

4. Opposite angles are equal

Q. In the figure, PQRS is a parallelogram, $PM\perp RSandRN\perp PS$. If PQ = l2cm, $PM=6cm$ and $RN=8cm,$ then the length of PS is equal to :

1. $9cm$
2. $12cm$
3. $18cm$
4. $4cm$

Q. The height of a parallelogram is one third of its base. If the area of the parallelogram is $192{\text{cm}}^2$, find its height and base.

Q. $ABCD$ is a parallelogram, $p$ is any point on $CD$. If $ar\left(DPA\right)=15c{m}^2$ and $ar\left(APC\right)=20c{m}^2$ then $ar\left(APB\right)=$

1. $15c{m}^2$
2. $20c{m}^2$
3. $35c{m}^2$
4. $30c{m}^2$

Q. In parallelogram ABCD, AB = $10$ cm, AD = $24$ cm and BD = $26$ cm, find the area of parallelogram(in cm${}^2$)

Q. The longer side of a parallelogram is $81cm$ and the corresponding altitude is $16cm$. If the length of shorter side is $24cm$ then the altitude corresponding to shorter side is

1. $36cm$
2. $54cm$
3. $48cm$
4. $24cm$

Q. ABCD is a parallelogram with sides AB = $12$ cm BC = $10$ cm and diagonal AC = $16$ cm The area of the parallelogram and the distance between the shorter sides are respectively

1. $120.5$ $c{m}^2$ ; $12.05$ cm
2. $119.8$ $c{m}^2$ ; $11.98$ cm
3. $118.71$ $c{m}^2$ ; $11.87$ cm
4. $117.9$ $c{m}^2$ ; $11.79$ cm

Q. Two adjacent sides of parallelogram are $24cm$ and $18cm$. If the distance between the longer sides is $12cm$; find the distance between the shorter sides.

1. $9cm$
2. $16cm$
3. $24cm$
4. Data insufficient

Q. In the figure, ABCD is a parallelogram, AB and BC are equal to 16 cm and 8 cm, respectively. If DF = 6 cm, what is the value of BE?

1. 8 cm
2. 12 cm
3. 10 cm
4. 16 cm

Q. One side of a parallelogram is 8 cm. If the corresponding altitude is 6 cm, then its area is given by

1. $48c{m}^2$
2. $40c{m}^2$
3. $36c{m}^2$
4. $24c{m}^2$

Q. The area of a parallelogram is $98{cm}^2$. If one altitude is half the corresponding base, determine the base and the altitude of the parallelogram.

Q. Question 4
In the figure, the area of parallelogram ABCD is:


A) AB $\times$ BM
B) BC $\times$ BN
C) DC $\times$ DL
D) AD $\times$ DL

Q. Write the following statements in 'if-then' form.
(i) The opposite angles of a parallelogram are congruent.
(ii) The diagonals of a rectangle are congruent.
(iii) In an isosceles triangle, the segment joining the vertex and the mid point of the base is perpendicular to the base.

Q. Find the area of parallelogram(in square m) whose base and altitude are given base$=1$m $5$cm, Altitude $=50$cm.

Q. In triangle ABC; D and E are mid-points of the sides AB and AC respectively. Through E, a straight line is drawn parallel to AB to meet BC at F. Prove that BDEF is a parallelogram. If AB = 16 cm, AC = 12 cm and BC = 18 cm, find the perimeter of the parallelogram BDEF.

Q. The adjacent sides of a parallelogram are $15cm$ and $10cm$. If the distance between the longer sides is $6cm$, find the distance between the shorter sides.

Q.
The area of a parallelogram ABCD is 98 $c{m}^2$. What is the area of the parallelogram EBCF if these two parallelograms have the same height? (in $c{m}^2$)

1. 49
2. 50
3. 98
4. None of the above

Q. Prove that:
Triangles on the same base and between the same parallels are equal in area.

Q. In the given figure find area of triangle ECF.

Q. DL and BM are the height on sides AB and AD respectively of parallelogram ABCD. If the area of the parallelogram is $1470$ $c{m}^2$, AB $=35$ and AD$=49$ cm, find the length of BM and DL.