Look at the statements given below: i. A parallelogram and a rect… - Vidyadip

MCQ

Look at the statements given below:
$i.$ A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
$ii.$ In a $\| gm \text{ABCD},$ it is given that $AB = 10\ cm.$
The altitudes $DE$ on $AB$ and $BF$ on $AD$ being $6\ cm$ and $8\ cm$ respectively, then $AD = 7.5\ cm.$
$iii.$ Area of a $\| gm =\frac{1}{2}\times\text{base}\times\text{altitude}.$
Which is true?

A
$I$ only
B
$II$ only
✓
$I$ and $II$
D
$II$ and $III$

✓

Answer

Correct option: C.

$I$ and $II$

Since the parallelogram and the rectangle are on the same base and between the same parallels, they are equal in area.
So, the statement $(I)$ is true.

$\operatorname{ar}(\| g m \text{ABCD})=A B \times D E=10 \times 6 \mathrm{\sim cm}^2$
Similarly,
$\operatorname{ar}(\| g m \mathrm{ABCD})=\mathrm{AD} \times \mathrm{BF}=\mathrm{AD} \times 8$
$\Rightarrow \mathrm{AD} \times 8=60$
$\Rightarrow \mathrm{AD}=7.5 \mathrm{\sim cm}$
So, $(II)$ is true.
$\operatorname{ar}(\| g m)=$ base $\times$ altitude
So, $(III)$ is false.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q" from AreaAreas of Parallelograms and Triangles→AreaAreas of Parallelograms and Triangles — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

In equation, $y = mx + c, m$ is:

Write the correct answer in the following:
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral $PQRS$, taken in order, is a rectangle, if:

In Fig , $P Q R S$ is a parallelogram. Can it be concluded that $\triangle R P S \cong \triangle Q S P$ ? Why or why not?

$AOB$ is the diameter of the circle. $ABCD$ is a cyclic trapezium in which $AB || DC.$ If $\angle\text{BED}=65^\circ,$ then $\angle\text{BDC}$ is equal to:

In fig if $DE = 8\ cm$, $\text{DE || BC}$ and $D$ is the mid-Point of $AB$, then the true statement is:

The ratio between the radius of the base and the height of a cylinder is $2 : 3.$ If its volume is $1617\ cm^3$, then its total surface area is:

$9^3+(-3)^3-6^3=?$

The maximum volume of a cone that can be carved out of a solid hemisphere of radius $‘r’$ is:

Between any two rational numbers there:

The perpendicular distance of the point $A(3, 4)$ from the $y-$axis is: