Figures on the Same Base and between the Same Parallels

Q. The side of a rhombus is 13 cm and the length of a diagonal is 24 cm.find the length of other diagonal.

Q. ABCD is a parallelogram and E and F are mid-points of AD and BC respectively. P is any point on AB. If area of ΔEDF = 16 $c{m}^2$, then find the area of ( ΔAEP+ ΔBFP)

1. 16 $c{m}^2$
2. 20$c{m}^2$
3. 26 $c{m}^2$
4. 30 $c{m}^2$

Q. A garden is in the shape of a rhombus with side 35 m and one diagonal 42 m. Find its area.

1. 2442 sq. m
2. 1296 sq. m
3. 1176 sq. m
4. 1024 sq. m

Q. In the adjoining figure, $\Delta QPR$ is right-angled at Q in which QR = 6 cm and PQ = 7 cm. Find the area of $\Delta QSR$, given that PS is parallel to QR.

1. $21c{m}^2$
2. $20c{m}^2$
3. $10c{m}^2$
4. $11c{m}^2$

Q. If the diagonals of a rhombus are 18 cm and 24 cm respectively, then its side is equal to

(a) 16 cm

(b) 15 cm

(c) 20 cm

(d) 17 cm

Q.

ABCD is a parallelogram in which CD is produced to P. DC = 6 cm and height BQ = 4 cm. Find the area of $△$ APB

1. 6 $c{m}^2$
2. 12 $c{m}^2$
3. 24 $c{m}^2$
4. 48 $c{m}^2$

Q.

Perimeter of a rhombus is 146cm and one diagonal is 55cm. Find the other diagonal and area of a rhombus.

Q.

Area of the parallelogram $ABCD=800$ sq. units. Find the area of $△AFC$. Here, $E$ and $F$ are the mid points of $AB$ and $AE$ respectively.

1. $50$ sq. units
2. $75$ sq. units
3. $100$ sq. units
4. $125$ sq. units

Q.

A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30m and it's longer diagonal is 48m how much area of the grass field will each cow be getting. ..

Q. In a parallelogram ABCD, M is the midpoint of side CD. A point N is chosen on DC extended such that, CN = MC and MN || AB What is the ratio of Area(ABCD):Area(ABNM)?

1. 3 : 1
2. 1 : 2
3. 2 : 1
4. 1 : 1

Q.

In the given figure, PQRS is a parallelogram If SM = MR and area $\Delta SPM=15c{m}^2$, then area parallelogram PQRS = ______ $c{m}^2$

1. 30
2. 45
3. 60
4. 90

Q.

Find the area of a rhombus one site of which measures 20 cm and diagonal 24 cm

Q.

Area of the parallelogram $ABCD=1024$ sq. units. Find the area of $△AGH$. Here $E,F,G$ and $H$ are the mid points of $AB,AD,AE$ and $AF$ respectively.

1. $32$ sq. units

2. $64$ sq. units

3. $100$ sq. units

4. $120$ sq. units

Q. Triangles on the same base and between the same parallels have equal area.

1. True
2. False

Q.

what is the area formula of rhombus ?

Q. In the given figures, mark the figures which are on the same base but not between same parallels.

1. 
2. 
3. 
4. 

Q. Mark (✓) against the correct answer in each of the following:
Each side of a rhombus is 10 cm long and one of its diagonals measures 16 cm. The length of the other diagonal is
(a) 6 cm
(b) 12 cm
(c) 13 cm
(d) $\sqrt{156}\mathrm{cm}$

Q. In the given figure ABCD is a quadrilateral in which diagonal BD = 64 cm, AL ⊥ BD and CM ⊥ BD such that AL = 16.8 cm and CM = 13.2 cm. Calculate the area of quadrilateral ABCD.

Q. The lengths of the diagonals PR and QS of a rhombus are 20cm and 48 cm. respectively, find the length of each side of the rhombus.

Q. A piece of land is in the shape of a rhombus ABCD in which each side measures 100 m and diagonal AC is 160 m long. Find the area of the rhombus.

Q.

A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?

Q. ABCD is a parallelogram in which CD is produced to P. DC = 6 cm and height BQ = 4 cm. Find the area of $△$ APB.


[3 Marks]

Q. What is the area of parallelogram ABCD with perpendicular BE lying on the base AD?

1. AB x AC
2. CB x CD
3. BE x BA
4. AD x BE

Q. A triangle and a parallelogram are on the same base and between the same parallel. The area of triangle is $54c{m}^2$. Find the area of parallelogram.

1. $54c{m}^2$
2. $108c{m}^2$
3. $28c{m}^2$
4. $27c{m}^2$

Q.

Area of the parallelogram $ABCD=800$ sq. units. Find the area of $△AFC$. Here, $E$ and $F$ are the mid points of $AB$ and $AE$ respectively.

1. $50$ sq. units
2. $75$ sq. units
3. $100$ sq. units
4. $125$ sq. units

Q. The area of $\Delta ABC$ is $400c{m}^2$. If AD is a median of $\Delta ABC$, then the area of $\Delta ABD$ is $200c{m}^2$.

1. False
2. True

Q. Show that the diagonals of a parallelogram divide it into four triangles of equal area.

Q.

A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of ₹5 per cm². Find the cost of painting.

1. ₹960
2. ₹480
3. ₹300
4. ₹192

Q. In the parallelogram $ABCD$ , the side $AB$ is produced to the point $X$, so that $BX=AB$ . The line $DX$ cuts $BC$ at $E$, then

1. True
2. False

Q. When two figures have a common base and are between 2 parallels, then one parallel must be the line containing .

1. the common base
2. a parallel base
3. uncommon base