# Area of a Parallelogram

## Trending Questions

**Q.**

A farmer wants to build a rectangular pen with $80$ feet of fencing. The pen will be built against the wall of the barn, so one side of the rectangle wont need a fence. What dimensions will maximize the area of the pen $?$

**Q.**

The area of the figure formed by joining the mid points of the adjacent sides of a thombus with diagonals 16 cm and 12 cm is

28cm2

48cm2

96cm2

24cm2

**Q.**

In rhe figure, ABCD and FECG are parallelograms equal in area. IF ar(△AQE)=12 cm2, then ar(||gmFGBQ) =

12cm2

20cm2

24cm2

36cm2

**Q.**ABCD is a quadrilateral and BD is one of its diagonals as shown in the following figure. Find the area of quadrilateral ABCD.

- 12 square units
- 73 square units
- 94 square units
- 21 square units

**Q.**

In the given figure, ABCD is parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

**Q.**

In a parallelogram ABCD, it is being given that AB=10 cm and the altitudes corresponding to the sides AB and AD are DL=6 cm and BM=8 cm, respectively.Find AD.

**Q.**

This question consists of two statements, namely, Assertion (A) and Reason (R).For selecting the correct answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

The correct answer is :(a) /(b) /(c) /(d)

**Q.**

In the figure , ABCD is a parallelogram. If AB = 12 cm, AE = 7.5 cm, CF = 15 cm, then AD =

3 cm

6 cm

8 cm

10.5 cm

**Q.**

ABCD is a parallelogram, G is the point on AB such that AG = 2 GB, E is a point of DC such that CE = 2 DE and F is the point of BC such that BF = 2 FC. Prove that:

(i)ar(ADEG)=ar(GBCE)(ii)ar(△EGB)−16ar(ABCD)(iii)ar(△EFC)=12ar(△EBF)(iv)ar(△EGB)=32ar(△EFC)

(v) Find what portion of the ara of parallelogram is the area of △EFG.

**Q.**

ABCD is a parallelogram. P is the mid point of AB. BD and CP intersect at Q such that CQ:QP=3:1.Ifar(△PBQ)=10cm2

Find the ara of parallelogram ABCD.

**Q.**Question 9

If the midpoints of the sides of a quadrilateral are joined in order, prove that the area of the parallelogram, so formed will be half of the area of the given quadrilateral (figure).

**Q.**

In th figure, ABCD, ABFE and CDEF are parallelograms. Prove that ar(△ADE)=ar(△BCF)

**Q.**

A, B, C, D are mid points of sides of parallelogram PQRS. IF ar(PQRS)=36cm2, then ar (ABCD) =

24cm2

18cm2

30cm2

36cm2

**Q.**

In the figure ABCD is a rectangle in which CD=6 cm, AD=8 cm.

Find the area of parallelogram CDEF.

**Q.**Question 4

In the figure, the area of parallelogram ABCD is:

A) AB × BM

B) BC × BN

C) DC × DL

D) AD × DL

**Q.**

In parallelogram ABCD, AB = 16 cm. The altitudes corresponding to sides AB and AD are respectively 8 cm and 10 cm. Then AD is equal to

12.5 cm

12.8 cm

15 cm

18 cm

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

- 7.25 cm
- 8.75 cm
- 10.25 cm
- 12 cm

**Q.**

The shape after joining the midpoints of sides of a rhombus will form :

Rectangle

Rhombus

Circle

Square

**Q.**

IF P is any point in the interior of a parallelogram ABCD, then prove that area of the triangle APB is less than half the area of parallelogram.

**Q.**Question 1

In the given figure, ABCD is parallelogram, AE⊥DC and CF⊥AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

**Q.**

In the given figure, ABCD is a ||gm in which AB=CD=5 cm and BD⊥DC such that BD=6.8 cm.Then, the area of ABCD=?

(a) 17 cm2

(b) 25 cm2

(c) 34 cm2

(d) 68 cm2

**Q.**

In the given figure, ABCD is a ||gm in which diagonals AC and BD intersect at O.If ar(||gm ABCD) is 52 cm2 then the ar(△ AOB)=?

(a) 26 cm2

(b) 18.5 cm2

(c) 39 cm2

(d) 13 cm2

**Q.**

In Q. No. 1, if AD = 6 cm, CF = 10 cm, AE = 8 cm , find AB.

**Q.**

The figure consists of 3 semicircles and an equilateral triangle of side 7 cm. Find the area of the entire figure.

253.25 cm

^{2}252.19 cm

^{2}134.75 cm

^{2}78.94 cm

^{2}

**Q.**Assertion: 3 + 7 = 9 is a statement.

Reason: A sentence that can be judged to be true or false, but not both, is called a statement.

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.

(c) Assertion is true and Reason is false.

(d) Assertion is false and Reason is true.

**Q.**In a parallelogram PQRS, PQ = 10 cm. The altitude corresponding to the sides PQ and SP are respectively 6 cm and 8 cm. Find SP

- 6 cm
- 15 cm
- 14 cm
- 7.5 cm

**Q.**

The adjacent sides of a parallelogram ABCD measures 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.

**Q.**

A parallelogram and a square have the same area. If the sides of the square measure 40 m and altitutde of the parallelogram measures 25 m, find the length of the corresponding base of the parallelogram.

**Q.**Assertion: A cyclic parallelogram is a square.

Reason: Diameter is the largest chord in a circle.

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.

(c) Assertion is true and Reason is false.

(d) Assertion is false and Reason is true.

**Q.**Assertion: Every parallelogram is a rectangle.

Reason: The angle bisectors of a parallelogram form a rectangle.

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.

(c) Assertion is true and Reason is false.

(d) Assertion is false and Reason is true.