(B) $(1)$ True: In a rhombus, all sides are equal. Perimeter $= 4 \times \text{side} = 4 \times 12 \, \text{cm} = 48 \, \text{cm}$.$(2)$ False: In a s

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(B) $(1)$ True: In a rhombus, all sides are equal. Perimeter $= 4 \times \text{side} = 4 \times 12 \, \text{cm} = 48 \, \text{cm}$.$(2)$ False: In a square $PQRS$, the diagonal $PR = s\sqrt{2}$, where $s$ is the side length. Given $PR = 8 \, \text{cm}$, then $s\sqrt{2} = 8 \implies s = 8 / \sqrt{2} = 4\sqrt{2} \, \text{cm}$. The perimeter is $4s = 4 \times 4\sqrt{2} = 16\sqrt{2} \, \text{cm}$, which is not $32 \, \text{cm}$.

Class 9 Mathematics Quadrilaterals Mix Examples - Quadrilaterals

Easy

State whether each of the following statements is true or false:
$(1)$ $ABCD$ is a rhombus. If $AB = 12 \, \text{cm}$, then the perimeter of $ABCD$ is $48 \, \text{cm}$.
$(2)$ $PQRS$ is a square. If $PR = 8 \, \text{cm}$, then the perimeter of $PQRS$ is $32 \, \text{cm}$.

A
True,True
B
True,False
C
False,True
D
False,False

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Mix Examples - Quadrilaterals

$ABCD$ is a trapezium in which $AB \parallel DC$ and $\angle A = \angle B = 45^{\circ}$. Find angles $C$ and $D$ of the trapezium.

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Three angles of a quadrilateral $ABCD$ are equal. Is it a parallelogram? Why or why not?

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In trapezium $ABCD$,$AB \parallel CD$. If $\angle A = 70^{\circ}$ and $\angle B = 85^{\circ}$,then $\angle D = \ldots$ (in $^{\circ}$)

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The diagonals $AC$ and $BD$ of a parallelogram $ABCD$ intersect each other at the point $O.$ If $\angle DAC = 32^{\circ}$ and $\angle AOB = 70^{\circ},$ then $\angle DBC$ is equal to: (in $^{\circ}$)

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In quadrilateral $ABCD$,$AC = BD$ and $AC \perp BD$. If $P, Q, R$ and $S$ are the midpoints of the sides $AB, BC, CD$ and $DA$ respectively,prove that $PQRS$ is a square.

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State whether each of the following statements is true or false:$(1)$ $ABCD$ is a rhombus. If $AB = 12 \, \text{cm}$, then the perimeter of $ABCD$ is $48 \, \text{cm}$.$(2)$ $PQRS$ is a square. If $PR = 8 \, \text{cm}$, then the perimeter of $PQRS$ is $32 \, \text{cm}$.

Similar Questions

$ABCD$ is a trapezium in which $AB \parallel DC$ and $\angle A = \angle B = 45^{\circ}$. Find angles $C$ and $D$ of the trapezium.

Three angles of a quadrilateral $ABCD$ are equal. Is it a parallelogram? Why or why not?

In trapezium $ABCD$,$AB \parallel CD$. If $\angle A = 70^{\circ}$ and $\angle B = 85^{\circ}$,then $\angle D = \ldots$ (in $^{\circ}$)

The diagonals $AC$ and $BD$ of a parallelogram $ABCD$ intersect each other at the point $O.$ If $\angle DAC = 32^{\circ}$ and $\angle AOB = 70^{\circ},$ then $\angle DBC$ is equal to: (in $^{\circ}$)

In quadrilateral $ABCD$,$AC = BD$ and $AC \perp BD$. If $P, Q, R$ and $S$ are the midpoints of the sides $AB, BC, CD$ and $DA$ respectively,prove that $PQRS$ is a square.

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State whether each of the following statements is true or false:
$(1)$ $ABCD$ is a rhombus. If $AB = 12 \, \text{cm}$, then the perimeter of $ABCD$ is $48 \, \text{cm}$.
$(2)$ $PQRS$ is a square. If $PR = 8 \, \text{cm}$, then the perimeter of $PQRS$ is $32 \, \text{cm}$.