# Exam Mission

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FUNDAMENTAL CONCEPTS
1. Results on Triangles:
1. Sum of the angles of a triangle is 180°.
2. The sum of any two sides of a triangle is greater than the third side.
3. Pythagoras Theorem:
In a right-angled triangle, (Hypotenuse)2 = (Base)2 + (Height)2.
4. The line joining the mid-point of a side of a triangle to the positive vertex is called the median.
5. 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.
6. In an isosceles triangle, the altitude from the vertex bisects the base.
7. The median of a triangle divides it into two triangles of the same area.
8. 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.
1. The diagonals of a parallelogram bisect each other.
2. Each diagonal of a parallelogram divides it into triangles of the same area.
3. The diagonals of a rectangle are equal and bisect each other.
4. The diagonals of a square are equal and bisect each other at right angles.
5. The diagonals of a rhombus are unequal and bisect each other at right angles.
6. A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
7. Of all the parallelogram of given sides, the parallelogram which is a rectangle has the greatest area.
IMPORTANT FORMULAE
1. 1.   Area of a rectangle = (Length x Breadth). Length = Area and Breadth = Area . Breadth Length
2.   Perimeter of a rectangle = 2(Length + Breadth).
2. Area of a square = (side)2 = (diagonal)2.
3. Area of 4 walls of a room = 2 (Length + Breadth) x Height.
4. 1.   Area of a triangle = x Base x Height.
2.   Area of a triangle = s(s-a)(s-b)(s-c)
where abc 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 semi-perimeter r = . s
5. 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.
6. 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
7. 1.   Circumference of a semi-circle = R.
 2.   Area of semi-circle = R2 . 2