**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}.

**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.

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/*√310.

**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 = πR**

^{2}, where R is the radius15.

**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) = (πR**

^{2}θ)/36018.

**Circumference of a semi-circle = πR**

19.

**Area of semi-circle = (πR**

^{2})/2**Quantitative Aptitude Quizzes and Study Material**

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