Important Formulas - Area - Tricks & Shortcuts

1. Results on Triangles
i. Sum of the angles of a triangle is 180°.
ii. The sum of any two sides of a triangle is greater than the third side.
iii. Pythagoras Theorem:
In a right-angled triangle, (Hypotenuse)2 = (Base)2 + (Height)2.
iv. The line joining the mid-point of a side of a triangle to the positive vertex is called the median.
v. The point where the three medians of a triangle meet, is called centroid. The centroid divided each of the medians in the ratio 2 : 1
vi. In an isosceles triangle, the altitude from the vertex bisects the base.
vii. The median of a triangle divides it into two triangles of the same area.
viii. The area of the triangle formed by joining the mid-points of the sides of a given triangle is one-fourth of the area of the given triangle.

i. The diagonals of a parallelogram bisect each other.
ii. Each diagonal of a parallelogram divides it into triangles of the same area.
iii. The diagonals of a rectangle are equal and bisect each other.
iv. The diagonals of a square are equal and bisect each other at right angles.
v. The diagonals of a rhombus are unequal and bisect each other at right angles.
vi. A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
vii. Of all the parallelogram of given sides, the parallelogram which is a rectangle has the greatest area.

Important Formulas
1.  Area of rectangle = (Length x Breadth)

2. Perimeter of a rectangle = 2(Length + Breadth).

3.  Area of a square = (side)2 = (1/2)(diagonal)2

4.  Area of 4 walls of a room = 2 (Length + Breadth) x Height.

5.  Area of a triangle =  (1/2)x Base x Height

6.   Area of a triangle =  √s(s-a)(s-b)(s-c                     (square root of s(s-a)(s-b)(s-c) )

7. Area of an equilateral triangle =(√3/4) x (side)2.

8.  Radius of incircle of an equilateral triangle of
side a = (a/(2√3))

9. Radius of circumcircle of an equilateral triangle of side a = a/√3

10. Radius of incircle of a triangle of area  Δ and semi-perimeter s = Δ/s

11.
Area of parallelogram = (Base x Height)

12. Area of a rhombus = ½ x (Product of diagonals)

13.  Area of a trapezium = ½ x (sum of parallel sides) x distance between them

14. Area of a circle = πR2, where R is the radius

15. Circumference of a circle = 2πR

16.   Length of an arc = (2πRθ)/360 , where
θ is the central angle

17. Area of a sector = ½  (arc x R) = (πR2θ)/360

18. Circumference of a semi-circle = πR

19. Area of semi-circle = (πR2)/2

Quantitative Aptitude Quizzes and Study Material

Quantitative Aptitude & Data Interpretation Topics & Formulas