FACTS AND FORMULAE FOR AREA QUESTIONS
FUNDAMENTAL CONCEPTS :
I. Results on Triangles:
1. Sum of the angles of a triangle is
2. The sum of any two sides of a triangle is greater than the third side.
3. Pythagoras Theorem : In a right - angled triangle,
4. The line joining the mid-point of a side of a triangle to the opposite vertex is called the median.
5. The point where the three medians of a triangle meet, is called Centroid. The centroid divides 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.
II.Results on Quadrilaterals :
1. The diagonals of a parallelogram bisect each other
2. Each diagonal of a parallelogram divides it into two 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.
1. Area of a rectangle = (length x Breadth)
2. Perimeter of a rectangle = 2( length + Breadth)
II. Area of square =
III. Area of 4 walls of a room = 2(Length + Breadth) x Height
1. Area of a triangle =
2. Area of a triangle = , where a, b, c are the sides of the triangle and
3. Area of an equilateral triangle =
4. Radius of incircle of an equilateral triangle of side
5. Radius of circumcircle of an equilateral triangle of side
6. Radius of incircle of a triangle of area and semi-perimeter
1. Area of a parallelogram = (Base x Height)
2. Area of a rhombus =
3. Area of a trapezium =
1. Area of a cicle = , where R is the radius.
2. Circumference of a circle = .
3. Length of an arc = , where is the central angle.
4. Area of a sector = =
1. Area of a semi-circle =
2. Circumference of a semi - circle =