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MATHEMATICS [2 Mark Question Answer]

Areas of Parallelograms and Triangles · ICSE STD 9 (ICSE - English Medium). 15 questions.

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[2 Mark Question Answer]

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15 questions · timed · auto-graded

Question 12 Marks
In the given figure, the area of $\triangle ABC$ is $64 cm^2$. State giving reasons :
(i) ar ( $\| gm ABCD$ )
(ii) ar (rect. ABEF).
Image
Answer
(i) $128 cm^2$
(ii) $128 cm^2$
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Question 22 Marks
In the adjoining figure, ABCD is a parallelogram. P is a point on DC such that ar $(\triangle APD )=25 cm^2$ and ar $(\triangle BPC )$ $=15 cm^2$. Calculate :(i) ar ( $\| gm ABCD$ )
(ii) $DP : PC$.
Image
Answer
(i) $80 cm^2$
(ii) $5: 3$
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Question 42 Marks
In the adjoining figure, ABCD is a parallelogram and O is any point on its diagonal AC.
Show that : $\operatorname{ar}(\triangle AOB )=\operatorname{ar}(\triangle AOD )$.
Image
Answer
[Hint. Join BD to intersect AC at P.]
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Question 52 Marks
In a $\| gm ABCD$, it is given that $AB =16 cm$ and the altitudes corresponding to the sides AB and AD are 6 cm and 8 cm respectively.
Find the length of AD .
Image
Answer
12 cm
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Question 62 Marks
In the given figure, ABCD is a parallelogram and P is a point on BC.
Prove that : $\operatorname{ar}(\triangle ABP )+\operatorname{ar}(\triangle DPC )=\operatorname{ar}(\triangle APD )$.
Image
Answer
[Hint. Draw $P Q\|A B\| D C$.]
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Question 72 Marks
In the given figure, $P$ is a point on side $B C$ of $\triangle A B C$ such that $BP : PC =1: 2$ and Q is a point on AP such that $PQ : QA =2: 3$.
Show that ar $(\triangle AQC ): \operatorname{ar}(\triangle ABC )=2: 5$..
Image
Answer
self
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Question 82 Marks
In the given figure, AD is a median of $\triangle ABC$ and P is a point on AC such that :
ar $(\triangle ADP ): \operatorname{ar}(\triangle ABD )=2: 3$.
Find : (i) $AP : PC \quad$ (ii) ar $(\triangle PDC )$ : ar $(\triangle ABC )$.
Image
Answer
(i) $2: 1$
(ii) $1: 6$
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Question 92 Marks
A parallelogram ABCD and a trapezium EFCD have the same base DC and are between the same parallels $l$ and $m$. If the length of $AB > length$ of EF , then compare the areas of ABCD and EBCD .
Image
Answer
$\operatorname{ar}( ABCD )>\operatorname{ar}( EBCD )$
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Question 102 Marks
Bansidhar is a farmer. He has a field in the form of a parallelogram ABCD. He took any point P on CD and joined it to points A and B. In how many parts the field is divided? What are the shapes of these parts? Bansidhar gave the three parts of the field to his two sons equally. How did he do it?
Answer
3 parts, triangles
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Question 122 Marks
In the given figure, $X Y\|B C, B E\| C A$ and $F C \| A B$.
Prove that: $\operatorname{ar}(\triangle ABE )=\operatorname{ar}(\triangle ACF )$.
Image
Answer
self
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Question 132 Marks
In the given figure, ABCD is a parallelogram and P is a point on BC.
Prove that: $\operatorname{ar}(\triangle ABP )+\operatorname{ar}(\triangle DPC )=\operatorname{ar}(\triangle APD )$.
Image
Answer
self
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Question 142 Marks
In the given figure, the area of $\triangle A B C$ is $64 cm^2$. State giving reasons :
(i) $\operatorname{ar}(\| \operatorname{gm} ABCD )$
(ii) ar (rect. ABEF )
Image
Answer
(i) $128 cm^2$
(ii) $128 cm^2$
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Question 152 Marks
Show that the line segment joining the mid-points of a pair of opposite sides of a parallelogram, divides it into two equal parallelograms.
Image
Answer
self
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[2 Mark Question Answer] - MATHEMATICS STD 9 Questions - Vidyadip