Question types

Mensuration question types

157 questions across 7 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

157
Questions
7
Question groups
5
Question types
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.

From a rectangular cardboard sheet 145 cm long and 32 cm broad, 42 circular plates each of diameter 8 cm have been cut out. Find the area of the remaining portion of the sheet.
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A wire when bent in the form of square, encloses an area of $146.41 cm^2$. If this wire is straightened and then bent to form a circle, what will be the area of the circle so formed?
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In a rectangular plot of land 70 m long and 40 m broad, a circular garden of radius 17.5 m is developed. Find the cost of turfing the remaining portion at the rate of ₹ 28.50 per sq. metre.
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Q 11[3 marks sum]3 Marks
Find the area of the shaded region in the adjoining figure, it being given that ABCD is a square of side $12 cm, CE =4 cm, FA =5 cm$ and $BG =5 cm$.
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Q 12[3 marks sum]3 Marks
Find the area of the shaded region of the adjoining figure, it being given that $\angle FAB =\angle CBA =90^{\circ}, ED \| AB \| FC , EG \perp FC , DH \perp FC$, $FG = HC , AB =15 cm, AF =9 cm, ED =8 cm$ and distance between AB and $ED =13 cm$.
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Q 14[3 marks sum]3 Marks
Find the area of the quadrilateral ABCD , given in the adjoining figure in which $AB =14 cm, BC =78 cm$, $CD =112 cm, BD =50 cm$ and $DA =48 cm$.
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Q 15[3 marks sum]3 Marks
Find the area of a quadrilateral ABCD whose diagonal AC is 25 cm long and the lengths of perpendiculars from opposite vertices B and D on AC are $BE =3.6 cm$ and $DF =2.4 cm$.
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Q 16[4 marks sum]4 Marks
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Q 17[4 marks sum]4 Marks
Kunal pulled out a string from one of his shoes. He found that it was 66 cm long. He bent it into different shapes one by one.
Q.1. If Kunal formed an equilateral triangle from the shoe string, what will be the length of each side of the triangle formed ?
(a) 11 cm $\quad$$\quad$(b) 13 cm$\quad$$\quad$(c) 22 cm$\quad$$\quad$(d) 33 cm
Q.2. If he formed a square from the string, the area of the square would be :
(a) $212.5 cm^2$$\quad$$\quad$ (b) $272.25 cm^2$ $\quad$$\quad$(c) $312.75 cm^2$$\quad$$\quad$ (d) $324 cm^2$
Q.3. He formed a circle from the string. Find the radius of the circle formed. [Use $\pi \frac{22}{7}$ ]
(a) 7 cm $\quad$$\quad$(b) 7.5 cm $\quad$$\quad$(c) 9 cm$\quad$$\quad$ (d) 10.5 cm
Q.4. The area of the circle formed from the string will be : [Use $\pi \frac{22}{7}$ ]
(a) $272.25 cm^2$$\quad$$\quad$(b) $346.5 cm^2$ $\quad$$\quad$(c) $414.75 cm^2$ $\quad$$\quad$(d) $452 cm^2$
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Q 29MCQ1 Mark
The length of each side of a square having area $A$ sq. units is
  • A
    $\frac{A}{l}$ units
  • B
    $\frac{ A }{4}$ units
  • $\sqrt{ A }$ units
  • D
    $2 \sqrt{A}$ units

Answer: C.

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Q 30MCQ1 Mark
Karan drew the side view of the staircase of a building as shown here. In the drawing, $A B C D$ is a rectangle of dimensions $8 cm \times 3 cm, D E F G$ is a square whose side is equal to double of CD and GHIJ is a rectangle in which GH $=4 A B$ and $H I=\frac{5}{4} B C$. The perimeter of the figure is :
Image
  • 72 cm
  • B
    90 cm
  • C
    45 cm
  • D
    36 cm

Answer: A.

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Q 31MCQ1 Mark
The breadth of a rectangle having area $A$ sq. units and length $l$ units is
  • $\frac{ A }{2}$ units
  • B
    $\frac{A^2}{l}$ units
  • C
    $\frac{A}{l^2}$ units
  • D
    $\frac{A^2}{l^2}$ units

Answer: A.

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Q 32MCQ1 Mark
Ravi and Manoj were finding the perimeter and area of a square plot of land. Ravi calculated the area and Manoj calculated the perimeter of the plot. Coincidently, they both got the same answer. The length of the side of the plotis :
  • A
    5 units
  • B
    2 units
  • C
    3 units
  • 4 units

Answer: D.

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