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**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.

**2.Pythagoras Theorem:**

(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.

**IMPORTANT FORMULAE**

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 R^{2}, 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 R^{2} /2 .

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