SsArea Important Formulas

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2/19/12 Area Important Formulas - Aptitude Questions and Answers

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Aptitude :: Area

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FUNDAMENTAL CONCEPTS

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.

2. Results on Quadrilaterals:

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- Albert Einstein

Overview

Important Formulas

Exercise

General Questions

Data Sufficiency 1

Data Sufficiency 2

Data Sufficiency 3

"I never think of the future. It comes soon enough."

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 FORMULAE

I. 1. Area of a rectangle = (Length x Breadth).

Length =Area

and Breadth =Area

.Breadth Length

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

II. Area of a square = (side)2= (diagonal)2.

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

IV. 1. Area of a triangle = x Base x Height.

2. Area of a triangle =s(s-a)(s-b)(s-c)

where a, b, care the sides of the triangle ands= (a+ b+ c).

3. Area of an equilateral triangle =3x (side)2.

4

4. Radius of incircle of an equilateral triangle of side a=a

.23

5. Radius of circumcircle of an equilateral triangle of side a=a.

3

6. Radius of incircle of a triangle of area and semi-perimeters=s

V. 1. Area of parallelogram = (Base x Height).

2. Area of a rhombus = x (Product of diagonals).

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

VI. 1. Area of a circle = R2, where R is the radius.

2. Circumference of a circle = 2 R.

3. Length of an arc =2 R

, where is the central angle.360

4. Area of a sector =1(arc x R)=

R2.

2 360

VII. 1. Circumference of a semi-circle = R.

2. Area of semi-circle = R2.2

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Area - Data Sufficiency 1



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