Question

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Answer 1

Answer:

Ratio of Area of Rectangle ABEF to Rectangle ACDF is 2 : 3

Area of rectangle ABEF is 10√41 units²

Perimeter of rectangle BCDE is ( 10 + 2√41 ) units²

Step-by-step explanation:

Given: ABEF and BCDE and ACDF are rectangles.

          coordinates of F( 5 , 2 ) , E( 11 , 10 ) , D( 14 , 14 ) and A( 0 , 6 )

To find: Ratio of Area of Rectangle ABEF to Rectangle ACDF

             Area of rectangle ABEF

             Perimeter of BCDE.

We know that, Area of Rectangle = Length × Width

In rectangle ABEF

length = FE = $\sqrt{(11-5)^2+(10-2)^2}=\sqrt{6^2+8^2}=\sqrt{36+64}=10\,units$

Width = FA

Area of Rectangle ABEF = FE × FA = ( 10 × FA ) units²

In rectangle ACDF

length = FD = $\sqrt{(14-5)^2+(14-2)^2}=\sqrt{9^2+12^2}=\sqrt{81+144}=15\,units$

Width = FA

Area of Rectangle ACDF = FD × FA = ( 15 × FA ) units²

$\frac{Area\:of\:Rectangle\:ABEF }{Area\:of\:Rectangle\:ACDF}=\frac{10\times FA}{15\times FA}=\frac{2}{3}$

Thus, Ratio of Area of Rectangle ABEF to Rectangle ACDF is 2 : 3

In rectangle ABEF

length = FE = 10 units    (from above)

Width = FA = $\sqrt{(0-5)^2+(6-2)^2}=\sqrt{(-5)^2+4^2}=\sqrt{25+16}=\sqrt{41}\,units$

Area of Rectangle ABEF = FE × FA = 10 × √41 = 10√41 units²

Thus, Area of rectangle ABEF is 10√41 units²

In rectangle BCDE

length = DE =  $\sqrt{(14-11)^2+(14-10)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5\,units$

Width = CD = FA = √41 units

Perimeter of Rectangle BCDE = 2 × ( DE + CD ) = 2 × (5 + √41) = ( 10 + 2√41 ) units²

Thus, Perimeter of rectangle BCDE is ( 10 + 2√41 ) units²

Answer 2

In the figure the ratio of the area of rectangle ABEF to the area of rectangle ACDF is 2/1.
For the rest we would need to know a unit of measurement, which is not provided with that you attached.