Area of a Parallelogram

Q.

Question 81

In the given figure, find the area of parallelogram ABCD, if the area of the shaded triangle is $9c{m}^2$

Q. What is the angle between the diagonals of a rhombus? [2 MARKS]

Q. PRSU is a rectangle with PQ = 6 cm, RS = 4 cm, SU = 16 cm. What is the area of the parallelogram QRTU?

1. 40 $c{m}^2$
2. 60 $c{m}^2$
3. 90 $c{m}^2$
4. 20 $c{m}^2$

Q.

A parallelogram has sides of length 12 cm and 8 cm. If the distance between the 12 cm sides is 5 cm. Find the distance between 8 cm sides. [4 MARKS]

Q.

• Two adjacent sides of a parallelogram are $24cm$ and $18cm$ if the distance between the longer side is $12cm$, find the distance between the shorter side.

Q.

PQRS is a parallelogram (see the given figure). QM is the height from Q to SR and QN is the height from Q to PS. If SR = 12 cm and QM = 7.6 cm. Find:

(a) the area of the parallelogram PQRS

(b) QN, if PS = 8 cm

Q. ABCD is a parallelogram, in which AB = 8 cm, AD = 6 cm and altitude AE = 4 cm. Find the altitude corresponding to the side [2 marks]

Q.

Find the corresponding height of a parallelogram corresponding to base $20cm$ if its area $=246c{m}^2$.

1. $6.12cm$
2. $12.3cm$
3. $1.26cm$
4. $11.12cm$

Q.

Two adjacent sides of a parallelogram are 51cm and 37cm. One of its diagonals is 20cm, then its area is _____.

1. $412c{m}^2$

2. $612c{m}^2$

3. $512c{m}^2$

4. $712c{m}^2$

Q.

Question 89

Perimeter of a parallelogram-shaped land is 96 m and its area is $270m^2$. If one of the side of this parallelogram is 18 m, find the length of the other side. Also, find the lengths of altitudes l and m in the given figure.

Q.

Find the missing values:

So No	Base	Height	Area of parallelogram
a.	20 cm	-	246 cm2
b.	-	15 cm	154.5 cm2
c.	-	8.4 cm	48.72 cm2
d.	15.6 cm	-	16.38 cm2

Q. Question 42

Fill in the blanks to make the statement true.

To find area, any side of a parallelogram can be chosen as ___ of the parallelogram.

Q. In a parallelogram, the base and corresponding height are in the ratio 3:2. If the area of the parallelogram is $216c{m}^2$, then find the measures its base and height.

1. 13 cm, 12 cm
2. 18 cm, 12 cm
3. 19 cm, 14 cm
4. 24 cm, 16 cm

Q. Area of a parallelogram is 24$c{m}^2$, if its base is 12cm find its height

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

Q.

Out of all those sweets, Ted likes kaju barfi the most. In the kaju barfi (parallelogram in shape) shown in the figure, can you find the area of the surface having silver covering?

1. 12 $c{m}^2$

2. 16 $c{m}^2$

3. 9 $c{m}^2$

4. 10 $c{m}^2$

Q.

Question 102

ABCD is a parallelogram in which AE is perpendicular to CD is shown in the given figure. Also, AC = 5 cm, DE = 4 cm and area of $\Delta AED=6c{m}^2$.
Find the perimeter and area of parallelogram ABCD.

Q. The base of a parallelogram is twice its height. If the area of the parallelogram is 512 cm², find the base and height.

Q. Sides of the parallelogram $ABCD$ are $5cm$ and $3cm$. The height corresponding to the base $CD$ is $4cm$. Find the height corresponding to the base $AD$.

1. $4cm$
2. $6.67cm$
3. $3cm$
4. $5cm$

Q.

Question 5 (a)

PQRS is a parallelogram QM is the height from Q to SR and QN is the height from Q to PS. If SR = 12 cm and QM = 7.6 cm. Find the area of the parallelogram PQRS

Q. The ratio of area of a parallelogram to perimeter of the parallelogram is $1:2$. Length of base of this parallelogram is 4 units and length of adjacent side to the base is 3 units. Find the height of the parallelogram.

1. $\frac{3}{4}$ unit
2. $\frac{5}{7}$ unit
3. $\frac{4}{7}$ unit
4. $\frac{7}{4}$ units

Q. Question 43

Fill in the blanks to make the statement true.

Perpendicular dropped on the base of a parallelogram from the opposite vertex is known as the corresponding ___ of the parallelogram.

Q.

Two equilateral triangles are merged together to form a rhombus. Find the perimeter of the rhombus formed if the length of a side of the equilateral triangle is 3 cm.

1. 15 cm

2. 12 cm

3. 3 cm

4. 9 cm

Q.

Write the two properties of the following quadrilaterals.

(a) rectangle

(b) trapezium

(c) rhombus

Q.

Perpendicular dropped on the base of a parallelogram from the opposite vertex is known as the corresponding _______ of the base.

Q. In a parallelogram ABCD, AB = 6 cm and BC = 4 cm. The height corresponding to the base AB is 3 cm. Find the area of the parallelogram.

1. $20c{m}^2$
2. $18c{m}^2$
3. $16c{m}^2$
4. $24c{m}^2$

Q.

In the newspaper you read about a football match between Brazil and Turkey. The country's were represented with their respective flags. You noticed a similar shape on Brazil's flag as kaju barfi. Length of the base of that shape is 10.6 m and height is equal to 8.3 m. So, the area of yellow parallelgram in the flag is $\_\_\_\_\_$ (rounded off to the nearest number).

Q. PQRS is a parallelogram. QM is the perpendicular height from Q to SR and QN is the perpendicular height from Q to PS. If SR$=12$cm and QM$=7.6$cm then find the area of the parallelogram PQRS.

Q. ABCD and PBCQ are rectangle and parallelogram respectively as shown in the figure. If AQ || BC and area of the rectangle ABCD is 10 $c{m}^2$, then find the area of the parallelogram PBCQ.

1. 20 $c{m}^2$
2. 10 $c{m}^2$
3. 5 $c{m}^2$
4. 15 $c{m}^2$

Q. If area of the parallelogram ABCD is 56 $m^2$, find the perimeter.

1. 44 m
2. 56 m
3. 60 m
4. 98 m

Q. Rotate the triangle ABC about vertex C by 120 degrees to form A'B'C' and choose the correct statement from the following:

1. Perimeter of the triangle increases by 2 times.
2. Coordinates of B and B' remains the same.
3. Angle A = Angle A'
4. Area of ABC is half the Area of A'B'C'.