we have to find the ratio of the area of triangle ABC to the area of sector BDCA .

You are watching: What is the ratio of the area of square abcf to the area of rectangle abde?      =9:4

Step-by-step explanation:

The relationship between area and side of triangle is

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

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

=9/4=(A1/A2)

=A1:A2=9:4

Ratio of areas =144:81

∴ ratio of sides =12:1

Let the longest side be x. Then

36:x=12:9 or x=1236×9=27cm

The sides of the regular hexagon ABCDEF can be posed as a. If so, the area of ABCDEF should be 6 times the are of the interior angle in the hexagon, considering there are 6 equilateral triangle that can fit in this regular 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 ABC should thus be the following -

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

As you can see, the area of ABC is half the area of ABCDEF, thus the ratio of the area of ABC to ABCDEF is 1 : 2

We have to find the" ratio of the area of sector ABC to the area of sector DBE".

Now,

the general formula for the area of sector is

Area of sector= 1/2 r²θ

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

For sector ABC, area= 1/2 (2r)²(β°)

= 1/2 *4r²*(π/180 β)

= 2r²(π/180 β)

For sector DBE, area= 1/2 (r)²(3β°)

= 1/2 *r²*3(π/180 β)

= 3/2 r²(π/180 β)

Now ratio,

Area of sector ABC/Area of sector DBE = = 4/3

C) 2/3Make a comparison, and do that by dividing the length if its a comparison of length or areas if its comparison of area and so on..To find the length, use the distance formula.Length of BC = 10Length of 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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