The area of a square and that of a square drawn on its diagonal are in the ratio:
- A$1:\sqrt{2}$
- ✓$1 : 2$
- C$1 : 3$
- D$1 : 4$
Answer: B.
View full solution →Question types
Mensuration question types
236 questions across 9 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
236
Questions
9
Question groups
5
Question types
01
M.C.Q. [1 Marks Each]
73 Q→02Assertion (A) & Reason (B) MCQ
4 Q→03True False[1 Marks ]
4 Q→04BLANKS [1 Marks Each]
5 Q→051 Marks Question
9 Q→062 Marks Questions
34 Q→075 Marks Questions
18 Q→08case /data -based (4 Marks)
2 Q→093 Marks Question
87 Q→Sample Questions
Mensuration questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The perimeters of a square and a rectangle are equal. If their areas be $\mathrm{A m}^2$ and $\mathrm{B} \mathrm{m}{ }^2$, then which of the following is a true statement?
- A$\text{A}<\text{B}$
- B$\text{A}\leq\text{B}$
- ✓$\text{A}>\text{B}$
- D$\text{A}\geq\text{B}$
Answer: C.
View full solution →The base and height of a triangle are $12m$ and $8m$ respectively. Its area is:
- A$96\text{m}^2$
- ✓$48\text{m}^2$
- C$16\sqrt{3}\text{m}^2$
- D$16\sqrt{2}\text{m}^2$
Answer: B.
View full solution →The area of a rhombus is $144\ cm^2$ and one of its diagonals is double the other. The length of the longer diagonal is:
- A$12\ cm$
- B$16\ cm$
- C$18\ cm$
- ✓$24\ cm$
Answer: D.
View full solution →On increasing each side of a square by $25\%$, the increase in area will be:
- A$25\%$
- B$55\%$
- C$40.5\%$
- ✓$56.25\%$
Answer: D.
View full solution →Assertion (A): The ratio of the circumference and the diameter of a circle is always constant.
Reason (R): The circumference of a circle having radius r is given by C = $2 \pi r$.
Reason (R): The circumference of a circle having radius r is given by C = $2 \pi r$.
- ✓Both Assertion (A) and Reason $(R)$ are true and Reason $(R)$ is the correct explanation of Assertion (A).
- BBoth Assertion (A) and Reason ( $R$ ) are true and Reason $(R)$ is not the correct explanation of Assertion (A).
- CAssertion ( $A$ ) is true but Reason ( $R$ ) is false.
- DAssertion (A) is false but Reason (R) is true.
Answer: A.
View full solution →Assertion (A): Area of a triangle $=\frac{1}{2} \times$ base $\times$ height.
Reason (R): Area of a triangle having sides $a, b, c=\sqrt{s(s-a)(s-b)(s-c)}$, where s = semi-perimeter of the triangle.
Reason (R): Area of a triangle having sides $a, b, c=\sqrt{s(s-a)(s-b)(s-c)}$, where s = semi-perimeter of the triangle.
- ABoth Assertion (A) and Reason $(R)$ are true and Reason $(R)$ is the correct explanation of Assertion (A).
- BBoth Assertion (A) and Reason ( $R$ ) are true and Reason $(R)$ is not the correct explanation of Assertion (A).
- ✓Assertion ( $A$ ) is true but Reason ( $R$ ) is false.
- DAssertion (A) is false but Reason (R) is true.
Answer: C.
View full solution →Assertion (A): Area of a parallelogram $=\frac{1}{2} \times$ product of two adjacent sides.
Reason (R): Area of a parallelogram = base x height.
Reason (R): Area of a parallelogram = base x height.
- ABoth Assertion (A) and Reason $(R)$ are true and Reason $(R)$ is the correct explanation of Assertion (A).
- BBoth Assertion (A) and Reason ( $R$ ) are true and Reason $(R)$ is not the correct explanation of Assertion (A).
- CAssertion ( $A$ ) is true but Reason ( $R$ ) is false.
- ✓Assertion (A) is false but Reason (R) is true.
Answer: D.
View full solution →Assertion (A): The area of the square formed by joining the midpoints of the sides of a square having area $64 cm^2$ is $16 cm^2$.
Reason (R): The diagonal of the square formed by joining the midpoints of the sides of a square is equal to the side of the outer square.
Reason (R): The diagonal of the square formed by joining the midpoints of the sides of a square is equal to the side of the outer square.
- ABoth Assertion (A) and Reason $(R)$ are true and Reason $(R)$ is the correct explanation of Assertion (A).
- BBoth Assertion (A) and Reason ( $R$ ) are true and Reason $(R)$ is not the correct explanation of Assertion (A).
- CAssertion ( $A$ ) is true but Reason ( $R$ ) is false.
- ✓Assertion (A) is false but Reason (R) is true.
Answer: D.
View full solution →Circumference of a circle $=2\pi\text{r}.$
View full solution →Area of a triangle = (base × height)
Area of a || gm = (base × height)
Area of a circle $=2\pi\text{r}^2.$
View full solution →1 hectare = __________ m2.
If l, b and h be the length, breadth and height respectively of a room, then area of its 4 walls = __________ sq units.
If d1 and d2 be the diagonals of a rhombus, then its are is __________ sq units.
If each side of a triangle is a cm, then its area = __________ cm2.
1 are = __________ m2.
Write $'T'$ for true and $'F'$ for false. Area of a circle $=2\pi\text{r}^2.$
View full solution →Write $'T'$ for true and $'F'$ for false. Area of $a\ ||\ gm$ = (base $\times $ height)
View full solution →Write $'T'$ for true and $'F'$ for false. Area of a triangle = (base $\times $ height)
View full solution →Write $'T'$ for true and $'F'$ for false.
Circumference of a circle $=2\pi\text{r}.$
View full solution →Circumference of a circle $=2\pi\text{r}.$
Fill in the blanks. If $l, b$ and $h$ be the length, breadth and height respectively of a room, then area of its $4$ walls = sq units.
View full solution →Find the area of the triangle in which Base $= 42\ cm$ and height $= 25\ cm.$
View full solution →Find the circumference of a circle whose radius is: $28\ cm.$
View full solution →Find the area of the square, the length of whose diagonal is: $72\ cm.$
View full solution →Find the area of the triangle in which Base $= 16.8\ m$ and Height $= 75\ cm.$
View full solution →Find the height of a parallelogram whose area is $54 \mathrm{~cm}^2$ and the base is $15\ cm.$
View full solution →The ratio of the radii of two circles is $4 : 5.$ Find the ratio of their areas.
View full solution →Find the area of a rhombus having each side equal to $13\ cm$ and one of the diagonals equal to $24\ cm.$
View full solution →The length and breadth of a park in the ratio $2 : 1$ and its perimeter is $240m.$ A path $2m$ wide runs inside it, along its boundary. Find the cost of paving the path at $Rs.80$ per $m^2$.
View full solution →In the given figure, a circle of diameter $21\ cm$ is given. Inside this circle, two circles with diameters $\frac{2}{3}$ and $\frac{1}{3}$ of the diameter of the big circle have been drawn, as shown in the given figure. Find the area of the shaded region. 
View full solution →The diameter of the wheel of a car is $77\ cm.$ How many revolutions will it make to travel $121\ km?$
View full solution →Krishna has a farmland in the shape of a rhombus PQRS as shown in the adjoining figure. The length of each side of this land is 450 m. Krishna fixed a wire PM such that $P M \perp Q R$ and another wire along the diagonal PR. He measured PM and PR and found that PM = 75m and PR = 125m He grew potatoes in the triangular region $\triangle P M R$ and sugarcane in the triangular region $\triangle P S R$. The remaining area was left for cattle rearing.
Q.1. The area of the farmland PQRS is
(a) $33,750 m^2$$\quad$(b) $56,250 m^2$
(c) $17,525 m^2$$\quad$(d) $9,375 m^2$
Q.2. The length of the diagonal QS of the rhombus PQRS is
(a) 360 m$\quad$(b) 450 m
(c) 480 m$\quad$(d) 540 m
Q.3. The area of the field used for growing potatoes is
(a) $3,750 m^2$$\quad$(b) $4,225 m^2$
(c) $6,250 m^2$$\quad$(d) $7.500 m^2$
Q.4. The area of the field used for growing sugarcane is
(a) $17,525 m^2$$\quad$(b) $9,375 m^2$
(c) $16,875 m^2$$\quad$(d) $10,250 m^2$
View full solution →Q.1. The area of the farmland PQRS is
(a) $33,750 m^2$$\quad$(b) $56,250 m^2$
(c) $17,525 m^2$$\quad$(d) $9,375 m^2$
Q.2. The length of the diagonal QS of the rhombus PQRS is
(a) 360 m$\quad$(b) 450 m
(c) 480 m$\quad$(d) 540 m
Q.3. The area of the field used for growing potatoes is
(a) $3,750 m^2$$\quad$(b) $4,225 m^2$
(c) $6,250 m^2$$\quad$(d) $7.500 m^2$
Q.4. The area of the field used for growing sugarcane is
(a) $17,525 m^2$$\quad$(b) $9,375 m^2$
(c) $16,875 m^2$$\quad$(d) $10,250 m^2$
Bimal has a flexible string which is 132 cm long. He bent it into different shapes one by one.
Q.1. Bimal bent the string to form an equilateral triangle. What will be the length of each side of the triangle formed?
(a) 11 cm$\quad$(b) 22 cm$\quad$(c) 44 cm$\quad$(d) 48 cm
Q.2. Bimal bent the string to form a square. Find the area of the square.
(a) $1,936 cm^2$$\quad$(b) $1,729 cm^2$$\quad$(c) $1,464 cm^2$$\quad$(d) $1,089 cm^2$
Q.3. He bent it into a circle. Find the radius of the circle formed. [Use $\pi=\frac{22}{7}$ ]
(a) 7.5 cm$\quad$(b) 10.5 cm$\quad$(c) 15 cm$\quad$(d) 21 cm
Q.4. The area of the circle formed by bending the string will be [Use $\pi=\frac{22}{7}$ ]
(a) $1,323 cm^2$$\quad$(b) $1,386 cm^2$$\quad$(c) $1,545 cm^2$$\quad$(d) $1,594 cm^2$
View full solution →Q.1. Bimal bent the string to form an equilateral triangle. What will be the length of each side of the triangle formed?
(a) 11 cm$\quad$(b) 22 cm$\quad$(c) 44 cm$\quad$(d) 48 cm
Q.2. Bimal bent the string to form a square. Find the area of the square.
(a) $1,936 cm^2$$\quad$(b) $1,729 cm^2$$\quad$(c) $1,464 cm^2$$\quad$(d) $1,089 cm^2$
Q.3. He bent it into a circle. Find the radius of the circle formed. [Use $\pi=\frac{22}{7}$ ]
(a) 7.5 cm$\quad$(b) 10.5 cm$\quad$(c) 15 cm$\quad$(d) 21 cm
Q.4. The area of the circle formed by bending the string will be [Use $\pi=\frac{22}{7}$ ]
(a) $1,323 cm^2$$\quad$(b) $1,386 cm^2$$\quad$(c) $1,545 cm^2$$\quad$(d) $1,594 cm^2$
Find the area ofa recta[gular plot, one side of whtch is $48m$ and lts diagonal is so $m.$
View full solution →Find the area of a right triangle whose base is $1.2m$ and hypotenuse $3.7m.$
View full solution →A diagonal of a quadrilateral is $26\ cm$ and the perpendiculars drawn to it from the opposite vertices are $12.8\ cm$ and $11.2\ cm$. Find the area of the quadrilateral.
View full solution →A room is $9m$ by $8m$ by $6.5m$. It has one door of dimensions $(2m \times 1.5m)$ and four windows each of dimensions $(1.5m \times 1m)$. Find the cost of painting the walls at $Rs 50$ per $m^2$.
View full solution →A $115$-m-long and $64-m$-broad lawn has two roads at right angles, one $2m$ wide, running parallel to its length, and the other $2.5m$ wide, running parallel to its breadth. Find the cost of gravelling the roads at $Rs 60$ per $m^2$.
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