Area Important Formulas:
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.
(i) In a right-angled triangle, (Hypotenuse)2 = (Base)2 + (Height)2.
(ii) The line joining the mid-point of a side of a triangle to the positive vertex is called the median.
(iii) 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.
(iv) In an isosceles triangle, the altitude from the vertex bisects the base.
(v) The median of a triangle divides it into two triangles of the same area.
(vi) 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.
3.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.
I. 1. Area of a rectangle = (Length x Breadth).
Length = (Area /Breadth) and Breadth = (Area /Length) .
2. Perimeter of a rectangle = 2(Length + Breadth).
II. Area of a square = (side)2 = 1/2(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, c are the sides of the triangle and s = 1/2(a + b + c).
3. Area of an equilateral triangle = √3 /4 x (side)2.
4. Radius of incircle of an equilateral triangle of side a = a/2√3 .
5. Radius of circumcircle of an equilateral triangle of side a =a = a/√3 .
6. Radius of incircle of a triangle of area and semi-perimeter r =Δ / s
V. 1. Area of parallelogram = (Base x Height).
2. Area of a rhombus = 1/2 x (Product of diagonals).
3. Area of a trapezium = 1/2 x (sum of parallel sides) x distance between them.
VI. 1. Area of a circle = pi x R2, where R is the radius.
2. Circumference of a circle = 2x pi x R.
VII. 1. Circumference of a semi-circle = pi x R.
2. Area of semi-circle = pi x R2 /2 .
Logarithm important formulas