Area of a Parallelogram

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

1. $28c{m}^2$
   

2. $48c{m}^2$
   

3. $96c{m}^2$
   

4. $24c{m}^2$
   

Q.

In rhe figure, ABCD and FECG are parallelograms equal in area. IF $ar\left(△AQE\right)=12c{m}^2,thenar\left(||gmFGBQ\right)$ =

1. $12c{m}^2$
   

2. $20c{m}^2$
   

3. $24c{m}^2$
   

4. $36c{m}^2$
   

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

1. $12squareunits$
2. $\frac{7}{3}squareunits$
3. $\frac{9}{4}squareunits$
4. $21squareunits$

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 =

1. 3 cm

2. 6 cm

3. 8 cm

4. 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:
$\left(i\right)ar\left(ADEG\right)=ar\left(GBCE\right)\left(ii\right)ar\left(△EGB\right)-\frac{1}{6}ar\left(ABCD\right)\left(iii\right)ar\left(△EFC\right)=\frac{1}{2}ar\left(△EBF\right)\left(iv\right)ar\left(△EGB\right)=\frac{3}{2}ar\left(△EFC\right)$
(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 $CQ:QP=3:1.Ifar\left(△PBQ\right)=10c{m}^2$
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 $ar\left(△ADE\right)=ar\left(△BCF\right)$

Q.

A, B, C, D are mid points of sides of parallelogram PQRS. IF $ar\left(PQRS\right)=36c{m}^2$, then ar (ABCD) =

1. $24c{m}^2$

2. $18c{m}^2$
   

3. $30c{m}^2$
   

4. $36c{m}^2$
   

Q.

In the figure $ABCD$ is a rectangle in which $CD=6cm,AD=8cm.$
Find the area of parallelogram $CDEF.$

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.

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

1. 12.5 cm

2. 12.8 cm

3. 15 cm

4. 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.

1. 7.25 cm
2. 8.75 cm
3. 10.25 cm
4. 12 cm

Q.

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

1. Rectangle

2. Rhombus

3. Circle

4. 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, $AE\perp DC$ and $CF\perp AD$. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

Q.

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

(a) $17c{m}^2$

(b) $25c{m}^2$

(c) $34c{m}^2$

(d) $68c{m}^2$

Q.

In the given figure, ABCD is a ||gm in which diagonals AC and BD intersect at O.If ar(||gm ABCD) is 52 $c{m}^2$ then the ar$\left(△AOB\right)$=?

(a) $26c{m}^2$

(b) $18.5c{m}^2$

(c) $39c{m}^2$

(d) $13c{m}^2$

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.

1. 253.25 cm²

2. 252.19 cm²

3. 134.75 cm²

4. 78.94 cm²

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

1. 6 cm
2. 15 cm
3. 14 cm
4. 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.