we have to discover the ratio of the area that triangle alphabet to the area of sector BDCA .

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=9:4

Step-by-step explanation:

The relationship in between area and side that triangle is

= (S1/S2)^2= (A1/A2)

=(3/2)^2=(A1/A2)

=9/4=(A1/A2)

=A1:A2=9:4

Ratio that areas =144:81

∴ ratio the sides =12:1

Let the longest side be x. Then

36:x=12:9 or x=1236×9=27cm

The political parties of the consistent hexagon ABCDEF have the right to be posed together a. If so, the area that ABCDEF need to be 6 time the space of the interior angle in the hexagon, considering there are 6 it is intended triangle that have the right to fit in this constant hexagon,

Area = 6( a * a * sin 60 ) / 2,

Area = ( about ) 2.6 sq units

Now applying cosine for triangle abc -

AC^2 = AB^2 + BC^2 – ( 2*AB*BC*cos 120 ),

a^2 + a^2 – ( 2a^2 * ( - 0.5 ) ) = a^2 + a^2+a^2 =3a^2,

AC = a√3

The area of alphabet should for this reason be the adhering to -

( a√3 * a√3 * sin 60 )/2 = 1.299038106 sq units

As you have the right to see, the area of abc is fifty percent the area of ABCDEF, thus the ratio of the area of abc to ABCDEF is 1 : 2

We have to discover the" ratio of the area the sector abc to the area of ar DBE".

Now,

the general formula for the area of sector is

Area the sector= 1/2 r²θ

where r is the radius and θ is the central angle in radian.

1° = π/180 rad

For ar ABC, area= 1/2 (2r)²(β°)

= 1/2 *4r²*(π/180 β)

= 2r²(π/180 β)

For ar DBE, area= 1/2 (r)²(3β°)

= 1/2 *r²*3(π/180 β)

= 3/2 r²(π/180 β)

Now ratio,

Area of ar ABC/Area of ar DBE =

= 4/3

C) 2/3Make a comparison, and do that by separating the size if its a comparison of length or areas if its to compare of area and so on..To find the length, usage the street formula.Length the BC = 10Length that BD = 1510/15 = 2/3
Ratio = A_ABC / A_BDCA = r^2/2 / 3/4(π)r^2 = 4 / 6π = 2 / 3π = 0.21

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