Concave Polygon
In a concave polygon, a line segment between two points on the boundary goes outside the polygon.
Or
In a concave polygon atleast one of the interior angle is more than \[180{}^\circ \]
Some Important Formulae
(i) Sum of all the angles in a convex polygon is\[\left( 2n\text{ }-\text{ }4 \right)\text{ }90{}^\circ \].
(ii) Exterior angle of a regular polygon is\[\frac{{{360}^{\circ }}}{n}\].
(iii) Interior angle of a regular polygon is \[\left( 180{}^\circ -\frac{360{}^\circ }{n} \right)\] where n is number of sides of the polygon
(iv) Number of diagonals of a convex polygon of n sides is \[\frac{n(n-3)}{2}\].
Quadrilaterals
A plane closed figured bounded by four segments is called quadrilateral.
1. The sum of four angles of a quadrilateral is equal to\[360{}^\circ \].
2. If the four vertices of a quadrilateral lie on the circumference of a circle i.e. if the quadrilateral can be inscribed in a circle it is called a cyclic quadrilateral. In a cyclic quadrilateral, the sum of opposite angles = c,
i.e.\[~A\text{ }+\text{ }C\text{ }=\text{ }180{}^\circ \text{ }and\text{ }B\text{ }+\text{ }D\text{ }=\text{ }180{}^\circ \]
Parallelogram
A quadrilateral having opposite sides are parallel is called a parallelogram. In a parallelogram,
(i) opposite sides are equal.
(ii) opposite angles are equal.
(iii) each diagonal divides the parallelogram into two congruent triangles.
(iv) sum of any two adjacent angles is\[180{}^\circ \].
(v) the diagonals bisect each other.
Rhombus
A parallelogram is a rhombus is which every pair of adjacent sides are equal (all four sides of a rhombus are equal).
Since, a parallelogram is a rhombus, all the properties of a parallelogram apply to a rhombus. Further, in a rhombus, the diagonals are perpendicular to each other.
Rectangle
A parallelogram is a rectangle in which each of the angles is equal to\[90{}^\circ \]. The diagonals of a rectangle are equal.
A rectangle is also a special type of parallelogram and hence all properties of a parallelogram apply to rectangles also.
Square
A rectangle is a square in which all four sides are equal (a rhombus in more... 
(a) 4080 \[c{{m}^{2}}\] (b) 5050 \[c{{m}^{2}}\]
(c) 6060 \[c{{m}^{2}}\] (d) 7070 \[c{{m}^{2}}\]
(e) None of these
Answer (b)
Explanation: Area of the given figure
\[=\frac{1}{2}\,\times \,30\times \,\,10\,+\,\frac{1}{2}\,\,20\,\times \,20\,+\,\frac{1}{2}\,\times \,40\,(30\,+\,40)\,+\,\frac{1}{2}\,\times \,\,40\]\[\left( 20+60 \right)+\frac{1}{2}\times 40\times 40\times \frac{1}{2}\times 60\times 30\text{ }c{{m}^{2}}\]
\[=\left( 150+200+1400+1600+800+900 \right)c{{m}^{2}}=5050\text{ }c{{m}^{2}}\]
Cuboid and Cube
A cuboid is a closed rectangular solid bounded by six rectangular faces. A cuboid has 12 edges and 8 vertices. The length, breadth and height of a cuboid is generally denoted by I, b and h respectively. A cuboid whose length, breadth and height are equal is called a cube and each equal side is called edge of the cube.
Co-ordinates of a Point
The pair of points which is used to describe the location of a point in two dimensional system are called co-ordinates of a point. The x- coordinate of a point is horizontal distance of the point from origin and y-coordinate of the point is the vertical distance from the origin.
Line Graph
A line graph is very useful for displaying data or information which changes continuously over a certain period of time. A line graph compares two variables. One variable is plotted along x-axis while another variable is plotted along y-axis.
Linear Graph
A linear graph is a graph which is used to represent the linear relationship between two variables. To draw a linear graph we use co-ordinates along x and y axis. The difference between a line graph or linear graph is that a line graph displays information as a series of points joined by line segments while a linear graph is always a straight line.
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