Area of Polygons

Q. Find the area of the following field. All dimensions are in metres.

1. $51400{\text{m}}^2$
2. $43400{\text{m}}^2$
3. $53000{\text{m}}^2$
4. $51200{\text{m}}^2$

Q.

Question 9

A regular hexagon is inscribed in a circle of radius r. The perimeter of the regular hexagon is
(a) 3 r (b) 6 r (c) 9 r (d) 12 r

Q.

Question 80

Find the area of the shaded portion in the following figure.

Q. Find the area of the given figure.

Q.

Given vertices $A(1,1),B(4,-2)$ and $C(5,5)$ of a triangle, then the equation of the perpendicular dropped from $C$ to the interior bisector of the angle $A$ is

1. $y–5=0$

2. $x–5=0$

3. $y+5=0$

4. $x+5=0$

Q.

Find the area of the shaded portion in the following figure.

Q.

The line $y=mx+1$ is a tangent to the curve $y^2=4x$ if the value of $m$ is ___________

Q.

Find the area of shaded portion.

Q.

You have$200\mathrm{feet}$ of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?

Q.

Area of a rhombus $=\frac{1}{2}$product of _________.

Q. Find the area of figure, if HD = 4 cm, GE = 5 cm, AF = BF = HF = 6 cm and CH = 7 cm.

1. 97 $c{m}^2$
2. 103 $c{m}^2$
3. 111 $c{m}^2$
4. 119 $c{m}^2$

Q.

Question 78

Find the area of the shaded portion in the following figure.

Q. Find the area of the following field. All dimensions are in metres.

1. $25100m^2$
2. $30100m^2$
3. $28850m^2$
4. $25300m^2$

Q.

Find the area of the pentagon shown in the figure if AD=10 cm, AG=8 cm, AH=6 cm, AF=5 cm and BF=5 cm, CG=7 cm and EH=3 cm.

Q.

The perimeter of a regular polygon of n side is given by:

1. n + (Side length)

2. 2n x (Side length)

3. 3n x (Side length)

4. n x (Side length)

Q.

Question 76

Find the area of the following field. All dimensions are in metres.

Q.

Find the area of the following field. All dimensions are in metres.

Q.

Question 82

Find the area of shaded portion.

Q. In the given pentagon, ratio of area of trapezium ABCD to area of $△$BEC is 5:2 and AG = 6 cm, EF = 4 cm. Find the length of BC if AD = 6 cm.

1. 6 cm
2. 8 cm
3. 9 cm
4. 10 cm

Q. Find the area of the rhombus if the measurements of the diagonals are 6 cm and 8 cm.

1. 24 $c{m}^2$
2. 40 $c{m}^2$
3. 20 $c{m}^2$
4. 30 $c{m}^2$

Q.

Find the area of a rectangle whose length and breadth are $18cm$ and $5cm$ respectively.

Q.

Find the area of hexagon PQRSTU in which QN is perpendicular to PS, RL is perpendicular to PS, TM is perpendicular to PS, UO is perpendicular to PS such that PO= 4m, ON=2m, NM= 6m, ML=2m, LS= 6m, UO= 6m, TM= 8m, QN= 2m, RL=4m.

__

Q. Question 10
There is a pentagonally shaped park as shown in the figure. For finding its area Jyoti and Kavita divided it in two different ways,

Find the area of this park using both ways. Can you suggest some other way of finding its area?

Q.

Which of the following methods are correct to find area of the hexagon?

1. Method-1

2. Method-2

3. Method-3

4. All of these

Q. In given pentagon area of trapezium BCDE is 2 times the area of $△$ABC. If AF = 3 cm, FG = 4 cm, and ED = 5 cm, then find area of pentagon.

1. 15 $c{m}^2$
2. 30 $c{m}^2$
3. 45 $c{m}^2$
4. 60 $c{m}^2$

Q. Two regular hexagons, each of side 30 cm are joined as shown in the fig. The perimeter of the new figure is

1. 365 cm
2. 360 cm
3. 330 cm
4. 355 cm

Q. Find the area of the rhombus if the measurements of the diagonals are 10 cm and 8 cm.

1. 40 $c{m}^2$
2. 30 $c{m}^2$
3. 60 $c{m}^2$
4. 80 $c{m}^2$

Q.

A point $P$ moves, so that the difference of its distances from $(-ae,0)$ and $(ae,0)$ is $2a$. Then, the locus of $P$ is

1. $\left(\frac{x^2}{a^2}\right)-\left(\frac{y^2}{a^2\left(e^2-1\right)}\right)=1$

2. $\left(\frac{x^2}{a^2}\right)+\left(\frac{y^2}{a^2\left(1-e^2\right)}\right)=1$

3. $\left(\frac{x^2}{a^2}\right)+\left(\frac{y^2}{a^2\left(1+e^2\right)}\right)=1$

4. $\left(\frac{x^2}{a^2}\right)-\left(\frac{y^2}{a^2\left(1+e^2\right)}\right)=1$

Q. What is the perimeter of a regular octagon of side length 7 cm?

Q.

Question 77

Find the area of the following field. All dimensions are in metres.