‘Railways RRB Geometry and Mensuration’ is a topic from where many questions are asked in railway exams. It is based on different types of shapes and figures. Shapes are mainly categorized into 2D and 3D. Those shapes which are having two dimensions are called 2D shapes. Those shapes which are having three dimensions are called 3D shapes. In this we have many different formulas through which the area, perimeter and volume of a shape can be calculated.
Square :
Perimeter of a Square = 4 $$\times$$ side of a square
Area of a Square = $$\text{(side of a square)}^{2}$$
Rectangle :
Perimeter of a Rectangle = 2(length+breadth)
Area of a Rectangle = length $$\times$$ breadth
Circle :
Diameter = $$2\times radius$$
Perimeter/Circumference of a Circle = $$2\times\pi\times radius$$
Area of a Circle = $$\pi \times (radius)^{2}$$
Right Angle Triangle:
Perimeter = hypotenuse+base+height
Area = $$\frac{1}{2}\times base \times height$$
Equilateral Triangle:
Perimeter = 3a
Area = $$\frac{\sqrt{3}}{4}\times a^{2}$$
Isosceles Triangle:
Perimeter = (2a+b)
Area = $$\frac{1}{2}\times b \times h$$
Scalene Triangle:
Perimeter = (a+b+c)
S = (a+b+c)/2
Area = $$\sqrt{S(S-a)(S-b)(S-c)}$$
Here a, b and c are the three sides of a triangle.
Note :: The sum of all the three angles of a triangle is equal to 180°.
Rhombus:
Perimeter = 4 $$\times$$ side
Area = $$\frac{1}{2}\times D_{1} \times D_{2}$$
Parallelogram:
Perimeter = $$2\times(l+b)$$
Area = $$b \times h$$
Trapezium:
Perimeter = p+q+r+s
Area = $$\frac{1}{2}\times h \times(p+r)$$
Q) The perimeter of a rectangle is 164 cm whose length is 44 cm, then find out the area of the rectangle.
Sol. The perimeter of a rectangle is 164 cm whose length is 44 cm.
$$2$$\times$$(44+breath) = 164$$
(44+breath) = 82
Breath = 82-44 = 38 cm
Area of the rectangle = $$44\times38$$
= 1672 $$cm^{2}$$
Q) If the ratio between the three angles of a triangle is 9:7:8, then find out the value of the third-largest angle.
Sol. If the ratio between the three angles of a triangle is 9:7:8.
9y+7y+8y = 180°
24y = 180°
y = 7.5°
Value of the third largest angle = 7y = $$7\times7.5°$$
= 52.5°