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.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.
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.
2. Results on Quadrilaterals
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)
Therefore length=(Area/Breadth) and Breadth = (Area/Length)
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
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