Sample Material of Online Coaching For SSC CGL (Tier - 2) - Area of Plane Figures
Sample Material SSC CGL TIER-2 Online Coaching
Numerical Aptitude (Chapter: Area of Plane Figures)
Area
The area of a plane figure is the measure of the surface enclosed by its boundary. The area of a triangle or a polygon is the measure of the surface enclosed by its sides.
1. Triangle
Area of the triangle =(1xBasexHeight)=1bh 2 2
where s = 1(a+b+c) 2
Perimeter of the triangle = a + b + c = 2s Radius of incircle of a triangle = ∆/s
2. Right-Angles Triangle
Area = 1bh
2
Hypotenuse, d =
(Pythagoras theorem) Perimeter = b + d + h
3. Isosceles Right-Angled Triangle
Area = 1(axa) =a2
2 2
Hypotenuse, d =
Perimeter = 2a +
4. Equilateral Triangle
Perimeter = 3a
Radius of incircle of an equilateral triangle of side a =
Radius of circumcircle of an equilateral triangle of side a =
5. Square
Area = (Side)2 = a2
= 1x(diagonal)2 2
Diagonal =
Perimeter = 4a
6. Rectangle
Area = Length × Breadth = l × b
Diagonal =
Perimeter = 2 (l + b)
Area of 4 walls = 2 (l +b) × h
7. Parallelogram
Opposite sides are parallel and equal and opposite angles are equal.
Area = Base × Height = b × h
Perimeter = 2 (a + b)
:: Home Assignment for Practice ::
1. The diagonal of a rectangle is thrice its smaller side. The ratio of the length to the breadth of the rectangle is:
(a) 4 : 1
(b)Ö3:1
(c)Ö2:1
(d)2Ö2:1
2. A rectangular carpet has an area of 120 sq. metres and a perimeter of 46 metres. The length of its diagonal is:
(a) 15 m
(b) 19 m
(c) 17 m
(d) 22 m
3. The diagonal of a rectangle is cm and its area is 20 sq. cm. The perimeter of the rectangle must be:
(a) 10 cm
(b) 18 cm
(c) 22 cm
(d) 42 cm
4. A took 15 seconds 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 sides walking at the rate of 68 m/min. The area of the field is:
(a) 52 m2
(b) 40 m2
(c) 61 m2
(d) 60 m2
5. A rectangular carpet has an area of 60 sq. m. If its diagonal and longer side together equal 5 times the shorter side, the length of the carpet is:
(a) 8 m
(b) 12 m
(c) 15 m
(d) 14.5 m