**SSC CHSL Topic Wise Study Material – Quantitative Aptitude – 2D-Mensuration**

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Mensuration is the branch of mathematics which deals with the study of measurement of geometric magnitudes like length, areas and volume for different geometric shapes.

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We classify this unit into two chapters

**1. 2D-Mensuration**

**2. 3D-Mensuration (We study 3D-Mensuration in next chapter)**

A number of questions are asked from this chapter every year which are formula based, by nature.

2D-Mensuration is also known as mensuration of plane figures. As we know plane figures have only length and breadth, so there are two features of 2D- figures, which we have to study in this chapter.

**Features of 2D-Figure**

**Area** Area is the total space enclosed by the boundary of a 2-dimensional figure. It is measured in square unit

**Perimeter** Sum of the sides of any enclosed figure is called the perimeter of that figure.

**Important Features and Formulae of Different 2D-Figure**

**Triangle** An enclosed figure formed from three line segments. A triangle has three angles with total sum of 180° and sum of its any two sides is more than the third side.

**Quadrilateral** A close figure having four sides is called a quadrilateral. A quadrilateral has four angles and sum of these angles is equal to 360°.

**Example The length of a room floor exceeds its breadth by 20 m. The area of the floor remains unaltered when the length is decreased by 10 m but the breadth is increased by 5 m. The area of the floor (in sq m) is ssc (10+2) 2011**

(a) 280

(b) 325

(c) 300

(d) 420

**Regular Polygon** In a regular polygons, all sides and all interior angles are equal.

**Example The ratio of the areas of a regular hexagon and an equilateral triangle having same perimeter is ssc (10+2) 2011**

(a) 2 : 3

(b) 6 : 1

(c) 3 : 2

(d) 1 : 6

**Circle** It is a plane figure enclosed by a curve on which every point is equally distant from a fixed point called centre inside the curve:

• Area = πr²

• Circumference (Perimeter) =2 πr

• Diameter = 2 r

• Length of the arc (l) =πrθ/180°

• Area of sector AOB =πr²θ/360°

r=radius

π=22/7

**For Circular Ring**

• Area = π(R²-π²)

• Difference in circumference of both the rings = (2πR- 2πr)

Where, R = radius of bigger ring; r= radius of smaller ring.

**Example Three circles of radii 4 cm, 6 cm and 8 cm touch each other pairwise externally. The area of the triangle formed by the line segments joining the centres of the three circles is SSC (10+2)2012**

(a) 6√6 sq cm

(b) 24√6 sq cm

(c)144√13 sq cm

(d) 12√105 sq cm

**Reference Corner**

** 1.An angle is twice its complementary angle. What is the measure of the angle? SSC (10 + 2) 2017**

(a) 30°

(b) 90°

(c) 60°

(d)120°

**2. The difference between the circumference and diameter of a circle is 150 m. The radius of that circle is SSC (10+2) 2014**

(a) 30 m

(b) 40 m

(c) 25 m

(d) 35 m

**3. The perimeter of a triangle is 54 m and its sides are in the ratio of 5 : 6 : 7. The area of the triangle is SSC (10 + 2) 2014**

(a)27√2 m²

(b)25 m²

(c) 18 m²

(d) 54√6m²

**4. The lengths of two parallel sides of a trapezium are 6 cm and 8 cm. If the height of the trapezium be 4 cm, then its area is SSC (10+2) 2014**

(a) 30 sq cm

(b)30cm

(c) 28 cm

(d)28sqcm

**5. If the ratio of an external angle and an internal angle of a regular polygon is 1 : 17, then the number of sides of the regular polygon is SSC (10+2) 2014**

(a) 36

(b) 12

(c) 20

(d) 18

**6. A bicycle wheel has a diameter (including the tyre) of 56 cm. The number of times the wheel will rotate to cover a distance of 2.2 km is**

(a) 1875

(b) 2500

(c) 625

(d) 1250

**7. The area of a square park is 25 sq km. The time taken to complete a round of the field once, at a speed of 3 km/h is SSC (10+2) 2014.**

(a)1h 60min

(b)4h 50min

(c)6h 10min

(d)5h 40min

**8. The perimeters of two similar triangles, ΔABC and ΔPQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then AB is SSC (10+2) 2014**

(a) 15cm

(b) 12cm

(c) 14cm

(d) 26cm

**9. If the sides of a right angled triangle tire three consecutive integers, then the length of the smallest side is SSC (10+2) 2014**

(a) 3 units

(b) 2 units

(c) 4 units

(d) 5 units

**10. The sum of the interior angles of a polygon is 1440°. The number of sides of the polygon is SSC (10 + 2) 2014**

(a) 6

(b) 9

(c) 10

(d) 12

**Practice Exercise**

**1. The length of a rectangle is twice its breadth, if the length is decreased by half of the 10 cm and the breadth is increased by half of the 10 cm, the area of the rectangle is increased by 5 sq cm more than 70 sq cm. Find the length of the rectangle.**

(a) 30 cm

(b) 40 cm

(c) 21 cm

(d) 45 cm

**2. The integral base of an isosceles triangle can be, whose area is 60 and the length of one of the equal sides in 13 cm.**

(a) 20 cm

(b) 10 cm

(c) 16 cm

(d) Data insufficient

**3. Area of circle is equal to the area of a rectangle having perimeter of 50 cm and the length is more than its breadth by 3 cm. What is the diameter of the circle?**

(a) 7 cm

(b) 21 cm

(c) 28 cm

(d) 14 cm

**4. The area of a rectangle is 4 times of the area of a square. The length of the rectangle is 90 cm and the breadth of the rectangle is 2/3 rd of the side of the square. What is the side of the square?**

(a) 10 cm

(b) 20 cm

(c) 15 cm

(d) Couldn’t be determined

**5. A ladder is resting with one end in contact with the top of a wall of height 60 m and the other end on the ground is at a distance of 11 m from the wall. The length of the ladder is**

(a) 61 m

(b) 71 m

(c) 87 m

(d) None of these

**6. The circumference of a circle is equal to the perimeter of a rectangle. The length and the breadth of the rectangle are 45 cm and 43 cm, respectively. What is the half the radius of the circle?**

(a) 56 cm

(b) 14 cm

(c) 28 cm

(d) 7 cm

**7. A circular wire of radius 42 cm is cut and bent in the form of a rectangle whose sides are in the ratio of 6 : 5. Find the 25% of the smaller side of the rectangle.**

(a) 15 m

(b) 18 m

(c) 20 m

(d) 19 m

**8. The base of a triangular field is three times its height. If the cost of cultivating the field is Rs 36.72 per hectare is Rs 495.72. Find the height and base of the triangular field.**

(a) 480 m, 1120 m

(b) 400 m, 1200 m

(c) 300 m, 900 m

(d) 250 m, 650 m

**9. A square park has each side 50 m. At each comer of the park, there is a flower bed in the form of a quadrant of radius 7 m, as shown in the figure. Find the area of remaining part of the park.**

(a) 2346 sq m

(b) 2340 sq m

(c) 2250 sq m

(d) 2155 sq m

**10. If the length of a rectangle is increased by 25% and the width is decreased by 20%, then the area of the rectangle**

(a) increase by 5%

(b) decrease by 5%

(c) remains unchanged

(d) increased by 10%

**11. The length of a rope by which a buffalo must be tethered, so that she may be able to graze a grassy area of 2464 sq m is**

(a)35m

(b)27m

(c)24m

(d)28m

**12. A took 15 s to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its side walking at the rate of 68m/min. The area of the field is **

(a) 30 m²

(b) 40 m²

(c) 50 m²

(d) 60 m²

**13. The area of a field in the shape of a trapezium measure 1440 m. The perpendicular distance between its parallel sides is 24 m. If the ratio of the parallel sides is 5 : 3 the length of the longer parallel sides is**

(a) 75 m

(b)45m

(c)120m

(d)60m

**14. If a piece of wire 25 cm long is bent into an arc of a circle subtending an angle of 75° at the centre, then the radius of the circle (in cm) is**

(a) π/120

(b) 60/π

(c) 60π

(d) None of these

**15. A prism has as the base a right angled triangle whose sides adjacent to the right angles are 10 cm and 12 cm long. The height of the prism is 20 cm. The density of the material of the prism is 6 g/cu cm. The weight of the prism is SSC (10+2) 2012**

(a) 3.4 kg

(b) 4.8 kg

(c) 6.4 kg

(d) 7.2 kg

**Answers**

**Hints & Solutions**

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