Regular polygons - class-VIII
Description: regular polygons | |
Number of Questions: 38 | |
Created by: Garima Pandit | |
Tags: maths rectilinear figures polygons geometric proof understanding shapes similar triangles introduction to trigonometry understanding elementary shapes understanding 3d and 2d shapes shapes and geometric reasoning polygon |
If $A+B=\dfrac{\pi}{3}$ and $\cos{A}+\cos{B}=1$, then which of the following is true
If $R$ is the radius of circumscribing circle of a regular polygon of $n$ sides, then $R =?$
Two consecutive vertices of a regular hexagon $A _1A _2A _3A _4A _5A _6$ are $A _1\equiv (1, 0), A _2\equiv (3, 0)$. If the centre of hexagon lies above the x-axis, then equation of the circumcircle of the hexagon is?
Let ${A} _{0}{A} _{1}{A} _{2}{A} _{3}{A} _{4}{A} _{5}$ be a regular hexagon inscribed in a circle of unit radius.Then the product of the length of ${A} _{0}{A} _{1}.{A} _{0}{A} _{2}.{A} _{0}{A} _{4}$ is
In the given regular hexagon of side $8\ cm$, six circles of equal radius are inscribe as shown in figure. The area of the unshaded region is $(in\ cm^{2})$
The area of a regular polygon of n sides is (where r is inradius, R is circumradius, and a is side of the triangle)
If the area of the pentagon $ABCDE$ be $\dfrac{45}{2}$ where $A = (1, 3), B = (-2, 5), C = (-3, -1), D = (0, -2)$ and $E = (2, t)$, then $t$ is:
If $r$ is the radius of the inscribed circle of a regular polygon of $n$ sides, then $r$ is equal to?
Area of the regular hexagon each of whose sides measures $1 \,cm$ is:
if $\frac { 1 }{ { a } _{ x }+1 } are\quad 8$ vertices of a rectengular octagon where ${ a } _{ k }\epsilon$ R, K =1,2,3,.....,8(where $ i =\sqrt { -1 } )$then area of the regular octagon is
in the given figure,BD is a side a regular hexagon,DC is a side of a regular pentagon and AD is a diameter calculate
What is the solid angle subtended by a hemisphere at its center?
The area of a regular polygon of $2n$ sides inscribed in a circle is given by?
If A B C D E F is a regular hexagon with A B = a and B C = b, then CE equals
If A B C D E F is a regular hexagon with A B = a and B C = b , then CE equals
If $\alpha$ is the angle which each side of a regular polygon of $n$ sides subtends at its centre, then $1 + \cos \alpha + \cos 2 \alpha + \cos 3 \alpha \ldots + \cos ( n - 1 ) \alpha$ is equal to
Relation between circumradius and number of sides is given by-
The sum of the radii of inscribed and circumscribed circles of an n sided regular polygon of side $'a'$ is
In $\Delta ABC$, there are 35 lines drawn parallel to the base BC such that each line divides the other side into, equal parts.
If BC =1.8 m find the length of $P _7 Q _7$.
For a regular hexagon with apothem $5m$, the side length is about $5.77m$. The area of the regular hexagon is (in $m^2$).
If $D$ is the midpoint of side $BC$ of a triangle $ABC$ and $AD$ is perpendicular to $AC$ then
If the angles of a triangle are in the ratio $2:3:7,$ then the sides opposite to these angles are in the ratio
In a triangle $ABC, \cos{A}+\cos{B}+\cos{C}=\dfrac{3}{2}$ then the triangle is
Let ${A} _{0}{A} _{1}{A} _{2}{A} _{3}{A} _{4}{A} _{5}$ be a regular hexagon inscribed in a circle of unit radius.The product of the length of the line segments ${A} _{0}{A} _{1},{A} _{0}{A} _{2}$ and ${A} _{0}{A} _{4}$ is
The ratio of the areas of two regular octagons which are respectively inscribed and circumscribed to a circle of radius $r$ is
If ${A} _{1}{A} _{2}{A} _{3}...{A} _{n}$ be a regular polygon of $n$ sides and
$\dfrac{1}{{A} _{1}{A} _{2}}=\dfrac{1}{{A} _{1}{A} _{3}}+\dfrac{1}{{A} _{1}{A} _{4}},$then
On the basis of the above information, answer the following questions:
If $r$ and $R$ are respectively the radii of the inscribed and circumscribed circles of a regular polygon of $n$ sides such that $\dfrac{R}{r}=\sqrt{5}-1$, then $n$ is equal to
The sum of inradius and circumradius of incircle and circumcircle of a regular polygon of side $n$ is
The sum of the radii of inscribed and circumscribed circles of an $n$ -sided regular polygon with side equal to one unit is?
Which polygon has no diagonals
If in a $\triangle ABC,{a}^{2}+{b}^{2}+{c}^{2}=8{R}^{2},$ where $R=$ circumradius,then the triangle is
In $\triangle ABC,$ which of the following statements are true:
There exist a triangle $ABC$ satisfying
If in a $\triangle ABC, \sin{C}+\cos{C}+\sin{\left(2B+C\right)}-\cos{\left(2B+C\right)}=2\sqrt{2}$, then $\triangle ABC$ is