Question

1. Find the area of the polygon based on the given measurements
SPAMS WILL REPORTED ​

Answer 1

Given:-

• MNORQ is a polygon.
• AM = 3 cm
• BR = 3 cm
• BC = 3 cm
• PD = 3 cm
• OC = 6 cm
• AN = 4 cm
• CD = 1 cm
• AB = 1 cm

To Find:-

• The Area of the Polygon.

Important Step:-

In the adjoining figure we need to find the measure of all the sides.

It is given that AB = 1 cm and BC = 3 cm

Hence,

AC = AB + BC = 3 + 1 = 4 cm

Also, it is given that PD = 3 cm and CD = 1 cm

Hence,

CP = CD + PD = 3 + 1 = 4 cm

It is given that, AB = 1 cm and AM = 2 cm

Hence,

MB = AB + AM = 1 + 2 = 3 cm

Also, it is given that BC = 3 cm and CD = 1 cm

Hence,

BD = BC + CD = 3 + 1 = 4 cm

Solution:-

We'll find the area step-by-step.

In the adjoining figure,

We can clearly see, that there are 4 right-angled triangle and two trapezium as follows:-

• ∆MAN
• ∆ PCO
• ∆QPD
• ∆RBM
• Trapezium ANOC
• Trapezium BRQD

In ∆MAN,

AM = 2 cm

AN = 4 cm

We know area of a triangle = $\sf{\dfrac{1}{2}\times base \times height}$

Hence,

$\sf{Area = \dfrac{1}{2}\times2\times 4}$

$\sf{Area = 4\:cm^2}$

Therefore, area of ∆MAN is 4 cm²

In ∆OCP,

PC = 4 cm

OC = 6 cm

$\sf{Area = \dfrac{1}{2}\times 4 \times 6}$

$\sf{Area = 12\:cm^2}$

Therefore, area of ∆OCP is 12 cm²

In ∆QPD,

QD = 2 cm

DP = 3 cm

$\sf{Area = \dfrac{1}{2}\times 2\times 3}$

$\sf{Area = 3\:cm^2}$

Therefore, area of ∆QPD is 3 cm².

In ∆RBM

MB = 3 cm

BR = 3 cm

$\sf{Area = \dfrac{1}{2}\times 3\times 3}$

$\sf{Area = 4.5\:cm^2}$

Therefore, area of ∆RBM is 4.5 cm²

In trapezium ANOC,

AC = 4 cm

AN = 4 cm

OC = 6 cm

We know,

Area of trapezium = $\sf{\dfrac{1}{2}(sum\:of\:parallel\:sides)\times height}$

Therefore,

$\sf{Area = \dfrac{1}{2}(4+6)\times4}$

$\sf{Area = 10\times 2}$

$\sf{Area = 20\:cm^2}$

Therefore, area of trapezium ANOC is 20 cm².

In trapezium BRQD,

BD = 4 cm

QD = 2 cm

BR = 3 cm

$\sf{Area = \dfrac{1}{2}(2+3)\times 4}$

$\sf{Area = 5\times 2}$

$\sf{Area = 10\:cm^2}$

Therefore, area of trapezium BRQD is 10 cm².

Now,

Area of polygon = Area of (∆MAN + ∆OCP + ∆PDQ + ∆BRM + trapezium ANOC + trapezium BRQD) sq.units

Therefore,

$\sf{Area_{(polygon)} = (4 + 12 + 3 + 4.5 + 20 + 10)\:cm^2}$

$\sf{Area_{(polygon)} = 53.5\:cm^2}$

Therefore, area of the polygon is 53.5 cm².

______________________________________

Answer 2

Answer:

a few is the right answer for your question.

c. All she wanted was______

moments on her own.

(few, a few, the few