Exercise :: Area  Important Formulas
 Area  Important Formulas
 Area  General Questions
 Area  Data Sufficiency 1
 Area  Data Sufficiency 2
 Area  Data Sufficiency 3
FUNDAMENTAL CONCEPTS

Results on Triangles:
Sum of the angles of a triangle is 180°.
The sum of any two sides of a triangle is greater than the third side.

Pythagoras Theorem:
In a rightangled triangle, (Hypotenuse)^{2} = (Base)^{2} + (Height)^{2}.
The line joining the midpoint of a side of a triangle to the opposite vertex is called the median.
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.
In an isosceles triangle, the altitude from the vertex bisects the base.
The median of a triangle divides it into two triangles of the same area.
The area of the triangle formed by joining the midpoints of the sides of a given triangle is onefourth of the area of the given triangle.

Results on Quadrilaterals:
The diagonals of a parallelogram bisect each other.
Each diagonal of a parallelogram divides it into triangles of the same area.
The diagonals of a rectangle are equal and bisect each other.
The diagonals of a square are equal and bisect each other at right angles.
The diagonals of a rhombus are unequal and bisect each other at right angles.
A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
Of all the parallelogram of given sides, the parallelogram which is a rectangle has the greatest area.
IMPORTANT FORMULAE

1. Area of a rectangle = (Length x Breadth).
Length = Area and Breadth = Area . Breadth Length 2. Perimeter of a rectangle = 2(Length + Breadth).

Area of a square = (side)^{2} = (diagonal)^{2}.

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

1. Area of a triangle = x Base x Height.
2. Area of a triangle = s(sa)(sb)(sc)
where a, b, c are the sides of the triangle and s = (a + b + c).3. Area of an equilateral triangle = 3 x (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 semiperimeter r = . s 
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.

1. Area of a circle = R^{2}, where R is the radius.
2. Circumference of a circle = 2R.
3. Length of an arc = 2R , where is the central angle. 360 4. Area of a sector = 1 (arc x R) = R^{2} . 2 360 
1. Circumference of a semicircle = R.
2. Area of semicircle = R^{2} . 2