Area of Parallelogram

Q. If the area of a parallelogram ABCD is 48 $c{m}^2$, find the length of AD and AB, if OP = 8 cm and CQ = 12 cm.

1. 3 cm, 2 cm
2. 6 cm, 4 cm
3. 8 cm, 6 cm
4. 12 cm, 8 cm

Q.

Question 80

Find the area of the shaded portion in the following figure.

Q.

A hall is in the shape of a parallelogram. One of the parallel walls measures 8 m. The perpendicular distance corresponding to that wall is 1.75 times the length of this wall. If the cost of carpeting the hall is ₹ 2 per $m^2$ . Find the total cost of carpeting the hall.

1. ₹ 264

2. ₹ 224

3. ₹ 642
4. ₹ 292

Q. Base and height of a parallelogram are in the ratio 5:3. Find the base and height of a parallelogram, if its area is 375$c{m}^2$.

1. 15 cm, 9 cm
2. 20 cm, 12 cm
3. 10 cm, 6 cm
4. 25 cm, 15 cm

Q. If area of a parallelogram is 29.6 sq cm and its base is 8 cm, find its height.

1. 3.7 cm
2. 4 cm
3. 4.1 cm
4. 3.8 cm

Q.

Find the perimeters and area of the parallelograms given in figure. [3 MARKS]

Q. Parallelograms on the same base and between the same parallel lines have equal areas.

1. True
2. False

Q. Find the area of a parallelogram whose base is 5 cm and height is 8 cm.
$\left[2\right]$

Q. A hall is in the shape of a parallelogram. One of the parallel walls measures 8 m. The perpendicular distance corresponding to that wall is 1.75 times the length of this wall. If the cost of carpeting the hall is Rs.2 per $m^2$ , find the total cost of carpeting the hall.

Q.

Ted with his friend Ned, was watching Mission Impossible. It was the climax scene, Ethan jumping from an aeroplane during the night. With the help of his gadgets, he got a blueprint of a parallelogram-shaped land he was about to land on and its measurements. Find the area of the place he can land to cheat death one more time by not falling in the rectangular killer swamp!

Q. $ABCD$ is a parallelogram whose height $DE$ is $4$ cm and base $AB$ is $10$ cm. If the height $AF$ on $BC$ is $5$ cm, find the width $BC$.

Q. Answer the following as per the exact requirement
$\left(i\right)$ $ABCD$ is a parallelogram in which $AB\parallel CD$ and $AB=CD=10cm$. If the perpendicular distance between $AB$ and $CD$ be $8cm$, find the area of the parallelogram $ABCD$
$\left(ii\right)$ $ABCD$ is a parallelogram having area $240c{m}^2$, $BC=AD=20cm$ and $BC\parallel AD$. Find the distance between the parallel sides $BC$ and $AD$.

1. $\left(i\right)50c{m}^2\left(ii\right)12cm$
2. $\left(i\right)80c{m}^2\left(ii\right)12cm$
3. $\left(i\right)70c{m}^2\left(ii\right)22cm$
4. $\left(i\right)60c{m}^2\left(ii\right)12cm$

Q. Find the base length of a parallelogram if the area is $96m^2$ and the corresponding height is 8 m.

1. 4 m
2. 8 m
3. 12 m
4. 24 m

Q. Find the area of a parallelogram whose base and corresponding height are 8 cm and 16 cm respectively.

1. 208 cm${}^2$
2. 128 cm${}^2$
3. 148 cm${}^2$
4. 168 cm${}^2$

Q. A parallelogram has sides of 20 cm and 30 cm. If the distance between its shorter sides is 15 cm; find the distance between the longer sides.

Q. A rectangle and a parallelogram have equal areas. If the sides of the rectangle are $10m$ and $12m$ and the base of the parallelogram is $20m$, then the altitude of the parallelogram is:

1. $7m$
2. $6m$
3. $5m$
4. $3m$

Q. The adjacent sides of a parallelogram have length $20cm$ and $12cm$. The distance between the two shorter sides is $5cm$. Find the area of parallelogram and the distance between the longer sides.

Q. Find the area of the parallelogram whose base is $17cm$ and height $0.8m$?

1. $1360c{m}^2$
2. $13.6c{m}^2$
3. $13.6m^2$
4. $1360m^2$

Q.

1. $960c{m}^2$
2. $860c{m}^2$
3. $280c{m}^2$
4. $130c{m}^2$
5. $1960c{m}^2$
   

Q. Question 57

State whether the statement is True or False.

In the given figure, perimeter of (ii) is greater than that of (i), but its area is smaller than that of (i).

Q.

Ted with his friend Ned, was watching Mission Impossible. It was the climax scene, Ethan Grunt jumping from a helicopter during night. With the help of his gadgets, he got a blue print of a parallelogram shaped land he was about to land on and its measurements. Find the area of the place he can land to cheat death one more time by not falling in the rectangular killer swamp!

1. 1200 m²

2. 1600 m²

3. 900 m²

4. 1000 m²

Q. In the given figure, ABCD is a parallelogram of area $1470{cm}^2.DL\perp AB$ and $BM\perp AD$ . If $AB=$35 $cm$ and $AD=$49$cm,$ find $DL$ and $BM$ .

Q. In the figure, ABCD is a rectangle and line MN cuts the rectangle into half. Triangle MNO and triangle MNP are identical triangles. The area of shaded region is ___________

1. more than 120 $c{m}^2$
2. Less than 120 $c{m}^2$
3. More than 180 $c{m}^2$
4. Equal to 120 $c{m}^2$

Q. Find the area of the parallelogram where one of its diagonals is of length $6.8cm$ and perpendiculars distance of this diagonal from the opposite vertex is of length $7.5cm$

1. $53c{m}^2$
2. $52c{m}^2$
3. $51c{m}^2$
4. $50c{m}^2$

Q. Find the area of a rhombus whose side is $5cm$ and whose altitude is $4.8cm$. If one of its diagonal is $8cm$ long, find the length of the other diagonal.

Q. Two sides of a parallelogram are 10 cm and 15 cm. If the altitude corresponding to the side of length 15 cm is 5 cm, then what is the altitude to the side of length 10 cm?

1. 5 cm
2. 7.5 cm
3. 10 cm
4. 15 cm

Q. Area of parallelogram ABCD (See the figure) is not equal to

1. $DE\times DC$
2. $BE\times AD$
3. $BF\times DC$
4. $BE\times BC$

Q. The height of a parallelogram is three-eights of its base. If the area of the parallelogram is $96c{m}^2$, find its height and base.

Q.

Statement 1: Perimeter of a rectangle is 2(length of one side + length of adjacent side).

Statement 2: Perimeter of any parallelogram can be given by 2(length of one side + length of adjacent side).

Pick the correct option.

1. Statement 1 is true and Statement 2 is false.

2. Both the statements are true and Statement 1 is a particular case of Statement 2.

3. Both the statements are true and Statement 2 is a particular case of Statement 1.

4. Statement 2 is not always true but Statement 1 is always true.

Q.

In the figure, ABCD is a parallelogram and AB = 6 cm. If the area of triangle ADE is $\frac{3}{4}$ that of parallelogram ABCD, then find the length of BE.