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# Area Formulas

### 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

I.  1. Area of a rectangle = (Length x Breadth).

2. Perimeter of a rectangle = 2(Length + Breadth).

II. Area of a square = (side)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 =

where a, b, c are the sides of the triangle and s = (a + b + c).

3.  Area of an equilateral triangle = x(side)²

4.  Radius of in circle of an equilateral triangle of side a =

5.   Radius of circumcircle of an equilateral triangle of side a =

6. Radius of incircle of a triangle of area and semi-perimeter s =

V.   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.

VI.    1.  Area of a circle = R² ,  where R is the radius.

2.   Circumference of a circle = 2R.

3.   Length of an arc = where is the central angle.

4. Area of a sector = (arc x R)=

VII. 1.   Circumference of a semi-circle = R.

2.   Area of semi-circle =

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