- Results on Triangles:
- Sum of the angles of a triangle is 180°.
- The sum of any two sides of a triangle is greater than the third side.
- Pythagoras Theorem:In a right-angled triangle, (Hypotenuse)2 = (Base)2 + (Height)2.
- The line joining the mid-point of a side of a triangle to the positive vertex is called the median.
- 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.
- In an isosceles triangle, the altitude from the vertex bisects the base.
- The median of a triangle divides it into two triangles of the same area.
- 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.
- Results on Quadrilaterals:
- The diagonals of a parallelogram bisect each other.
- Each diagonal of a parallelogram divides it into triangles of the same area.
- The diagonals of a rectangle are equal and bisect each other.
- The diagonals of a square are equal and bisect each other at right angles.
- The diagonals of a rhombus are unequal and bisect each other at right angles.
- A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
- 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).
Length = Area and Breadth = Area . Breadth Length
2. Perimeter of a rectangle = 2(Length + Breadth).
- Area of a square = (side)2 = (diagonal)2.
- Area of 4 walls of a room = 2 (Length + Breadth) x Height.
- 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 = (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
- 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.
- 1. Area of a circle = R2, where R is the radius.2. Circumference of a circle = 2R.
3. Length of an arc = 2R , where is the central angle. 360 4. Area of a sector = 1 (arc x R) = R2 . 2 360
- 1. Circumference of a semi-circle = R.
2. Area of semi-circle = R2 . 2
Area – General Questions