Question 1 :
The area of a right angled triangle is $20\:cm^2$ and one of the sides containing the right angle is 4 cm. The altitude on the hypotenuse is
Question 2 :
A rectangle and a rhombus are on the same base and between the same parallels. The ratio of their areas is :
Question 3 :
For $a,b,c,d\in N$, the area of the parallelogram bounded by the lines $y=ax+c,y=ax+d,y=bx+c$ and $y=bx+d$ is $18$ while the area of the parallelogram bounded by the lines $y=ax+c,y=ax-d,y=bx+c$ and $y=bx-d$ is $72$. The least possible value of $a+b+c+d$ will be:
Question 5 :
Two parallelograms are on the same base and between the same parallels. The ratio of their areas is :<br/>
Question 6 :
ABC is a right angled at B with $BC = 6$ and $AC = 10\ cm$. Also $\triangle ABC$ and $\triangle BCD$ are on the same base $BC$. Find $ar (\triangle BCD)$.
Question 7 :
Given two parallelogram $ABCD$ and $CDEF$ on the same base $CD. $The height of parallelogram $ABCD$ is same as the height of parallelogram $CDEF.$ Area of  $ABCD$ is $50 m^{2}$. Find the area of parallelogram $CDEF.$
Question 9 :
For $3$ parallelograms, $A$, $B$ and $C$, parallelograms $A$ and $B$ shares same base $l$ and lie along same parallels $l$ and $m$. Similarly the parallelograms $B$ and $C$ shares the same base $m$ and between the same parallels. The area of all three parallelograms will be equal.
Question 10 :
Assertion: The area of a parallelogram and a rectangle having a common base and between same parallels are equal.
Reason: Another name of a rectangle is a parallelogram.
Question 11 :
One side of a parallelogram is $16\ cm$ and the distance of this side from the opposite side is $4.5\ cm$. The area of the parallelogram is
Question 12 :
$PQRS$ is the smallest square whose vertices are on the respective sides of the square $ABCD$. The ratio of the areas of $\square PQRS$ to $\square ABCD$ is
Question 13 :
Two parallelograms are on equal bases and between the same parallels. The ratio of their areas is :<br/>
Question 14 :
The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is
Question 15 :
The mid-point of the sides of a triangle along with any of the vertices as the fourth point make a parallelogram of area equal to
Question 16 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d100f59b460d7261f3a8.png' />
In the above figure, the area of parallelogram ABCD is
Question 17 :
The area of the figure formed by joining the mid-points of the adjacent sides of a rhombus with diagonals 12 cm and 16 cm is
Question 18 :
State whether the statement is TRUE or FALSE: If medians of a triangle ABC intersects at G, then $ar\left(AGB\right)=ar\left(AGC\right)=ar\left(BGC\right)=\frac{1}{3}ar\left(ABC\right)$.
Question 19 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d10df59b460d7261f3ba.jpg' />
In the above figure, if X and Y are the mid-points of AC and AB respectively,QP|| BC and CYQ and BXP are straight lines. Then $ar\left(\triangle ABP\right)=ar\left(\triangle ACQ\right)$. State whether the statement is TRUE or FALSE.
Question 20 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d10af59b460d7261f3b6.jpg' />
In the above figure, if the mid-points of the sides of a quadrilateral are joined in order, then will the area of the parallelogram so formed be half of the area of the given quadrilateral?
Question 21 :
State whether the statement is TRUE or FALSE: Parallelograms on equal bases and between the same parallels are equal in area.
Question 23 :
ABCD is a quadrilateral whose diagonal AC divides it into two parts, equal in area, then ABCD
Question 24 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d109f59b460d7261f3b4.jpg' />
In the above figure, ABCD is a parallelogram in which BC is produced to E such that CE = BC. AE intersects CD at F. If ar (DFB) = 3 $cm^2$, find the area of the parallelogram ABCD.
Question 25 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d107f59b460d7261f3b2.jpg' />
In the above figure, O is any point on the diagonal PR of a parallelogram. Is ar (PSO) = ar (PQO)?
Question 26 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d10bf59b460d7261f3b8.png' />
In the above figure, ABCDE is any pentagon. BP drawn parallel to AC meets DC produced at P and EQ drawn parallel to AD meets CD produced at Q. Is ar (ABCDE) = ar (APQ)?
Question 27 :
A point E is taken on the side BC of a parallelogram ABCD. AE and DC are produced to meet at F. Is ar (ADF) = ar (ABFC)?
Question 28 :
Two parallelograms are on equal bases and between the same parallels. The ratio of their areas is
Question 29 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d101f59b460d7261f3a9.jpg' />
In the above figure, if parallelogram ABCD and rectangle ABEM are of equal area, then
Question 30 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d10ef59b460d7261f3bc.jpg' />
In the above figure, ABCD is a parallelogram. Points P and Q on BC trisects BC in three equal parts. Is $ar\left(APQ\right)$ = $ar\left(DPQ\right)$ = $\frac{1}{6}ar\left(ABCD\right)$?
Question 31 :
State whether the statement is TRUE or FALSE: A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
Question 32 :
State whether the statement is TRUE or FALSE: Two congruent figures have equal areas but the converse is not always true.
Question 33 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d105f59b460d7261f3af.jpg' />
In the above figure, D is the mid-point of AB and P is any point on BC. If $CQ\ \parallel\ PD$ meets AB in Q, then $ar\left(\triangle BPQ\right)=\frac{1}{2}ar\left(\triangle ABC\right)$.
