Question 1 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d111f59b460d7261f3c1.jpg' />
In the above figure, PQRS is a square. T and U are respectively, the mid-points of PS and QR. Find the area of $\triangle{OTS}$, if PQ = 8 cm, where O is the point of intersection of TU and QS.
Question 2 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d10ff59b460d7261f3bd.jpg' />
In the above figure, $l$, $m$, $n$ are straight lines such that and $n$ intersects $l$ at P and $m$ at Q. ABCD is a quadrilateral such that its vertex A is on $l$. The vertices C and D are on $m$ and $AD\ \parallel\ n$. Is ar (ABCQ) = ar (ABCDP)?
Question 3 :
State whether the statement is TRUE or FALSE: Parallelograms on the same base and between the same parallels are equal in area.
Question 4 :
State whether the statement is TRUE or FALSE: Triangles with equal bases and equal areas have equal corresponding altitudes.
Question 5 : <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 6 : <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 7 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d111f59b460d7261f3c0.jpg' />
In the above figure, ABCD is a parallelogram and BC is produced to point Q such that AD = CQ. If AQ intersects DC at P. Is ar (BPC) = ar (DPQ)?
Question 8 :
State whether the statement is TRUE or FALSE: Parallelograms on equal bases and between the same parallels are equal in area.
Question 9 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d10df59b460d7261f3bb.jpg' />
In the above figure,ABCD and AEFD are two parallelograms. Then $ar\left(\triangle PEA\right)=ar\left(\triangle QFD\right)$. State whether the statement is TRUE or FALSE.
Question 10 :
In which of the following figures, you find two polygons on the same base and between the same parallels?
Question 11 :
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 12 :
State whether the statement is TRUE or FALSE: The area of a triangle is equal to one-half of the area of a rectangle/parallelogram of the same base and between same parallels.
Question 13 : <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 14 :
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 15 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d106f59b460d7261f3b0.png' />
In the above figure, ABCD is a parallelogram whose area is 90 $cm^2$. Find ar (ABD).
Question 16 :
The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is
Question 17 : <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 18 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d106f59b460d7261f3b1.png' />
In the above figure, ABCD is a parallelogram whose area is 90 $cm^2$. Find ar (BEF).
Question 19 :
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 20 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d104f59b460d7261f3ae.png' />
In the above figure, ABCD is a parallelogram whose area is 90 $cm^2$. Find ar (ABEF).
Question 21 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d108f59b460d7261f3b3.jpg' />
In the above figure, ABCD is a square. E and F are respectively the mid-points of BC and CD. If R is the mid-point of EF. Is $ar\left(\triangle AER\right)=ar\left(\triangle AFR\right)$?
Question 22 :
State whether the statement is TRUE or FALSE: If ∆ ABC ≅ ∆ PQR, then ar (∆ ABC) = ar (∆ PQR).
Question 23 : <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 24 :
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 25 :
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 26 : <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 27 :
ABCD is a quadrilateral whose diagonal AC divides it into two parts, equal in area, then ABCD
Question 28 : <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 29 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d103f59b460d7261f3ac.jpg' />
In the above figure, PSDA is a parellelogram. Points Q and R are taken on PS such that PQ = QR = RS and $PA\ \parallel\ QB\ \parallel\ RC$. Is ar (PQE) = ar (CFD)?
Question 30 :
The medians BE and CF of a triangle ABC intersects at G. Is the area of $\triangle GBC=$area of the quadrilateral AFGE?
Question 31 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d10ff59b460d7261f3be.jpg' />
In the above figure, $BD\ \parallel\ CA$. E is the mid pointof CA and $BD=\frac{1}{2}CA$. Is ar (ABC) = 2ar (DBC)?
Question 32 :
The diagonals of a parallelogram ABCD intersects at a point O. Through O, a line is drawn to intersect AD at P and BC at Q. Does PQ divide the parallelogram into two parts of equal area?
Question 34 : <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 35 :
State whether the statement is TRUE or FALSE: Two congruent figures have equal areas but the converse is not always true.
Question 36 :
State whether the statement is TRUE or FALSE: A diagonal of a parallelogram divides the parallelogram in two triangles of equal area.
Question 37 :
Two parallelograms are on equal bases and between the same parallels. The ratio of their areas is
Question 38 :
State whether the statement is TRUE or FALSE: If a triangle and a parallelogram are on the same base and between the same parallels, the area of the triangle is equal to one-half area of the parallelogram.
Question 39 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d104f59b460d7261f3ad.jpg' />
In the above figure, X and Y are points on the side LN of triangle LMN such that LX = XY = YN. If X, a line is drawn parallel to LM to meet MN at Z. State TRUE or FALSE that: ar (LZY) = ar (MZYX).
Question 40 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d109f59b460d7261f3b5.jpg' />
In the above figure, ABCD is a trapezium with $AB\ \parallel\ DC$ and L is the mid-point of BC. Through L, a line $PQ\ \parallel\ AD$ has been drawn which meets AB in P and DC produced in Q. Is ar (ABCD) = ar (APQD)?
Question 41 :
If a triangle and a parallelogram are on the same base and between same parallels, then the ratio of the area of the triangle to the area of parallelogram is
Question 42 : <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 $ar\left(\triangle BPQ\right)=\frac{1}{2}ar\left(\triangle ABC\right)$.
Question 43 :
State whether the statement is TRUE or FALSE: Triangles on the same base and between the same parallels are equal in area.
Question 44 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d102f59b460d7261f3aa.jpg' />
In the above figure, ABCD is a trapezium with parallel sides AB$=a\ cm$ and DC$=b\ cm$. E and F are the mid points of the non parallel sides. The ratio of ar(ABFE) and ar(EFCD) is
