In the diagram, △ABC∼△CDE. Write an equation for line k

Step-by-step explanation:

Line AB is parallel to line CD (k) so they have the same slope.

slope=m=(y2-y1)/(x2-x1)

m=(6-0)/(4-0)

m=6/4=1.5

y=mx+b, we know m=1.5 so

y=1.5x+b, and we know it passes through point (4,0) so we can solve for b

0=1.5(4)+b

0=6+b

b=-6 so line k is

y=1.5x-6

Step-by-step explanation:

Hello, I think  I can help you with this

let's remember the area of a rectangle

Area(r) =length * width

and, the area of a triangle is

Area (t)=(base* height)/2

Step 1

find the area of the triangle

the triangles are similar, so

Base=10 cm

height=8.7 cm

Hence,

Area(t)=(10 cm*8.7 cm)/2

Area(t)=43.5 cm2

Step 2

find the area of the rectangle

the rectangles are similar, so

length=10 cm

width=8 cm

Hence,

Area(r)=(10 cm*8. cm)

Area(r)=80 cm2

Step 3

Add

there are 2 triangles and 3 rectangles, so the total area is

Total area=2 *Area(t)+3*Area(r)

put the values into the equation

Total area=2*43.5 cm2+3*80 cm2

Total area=87 cm2+ 240 cm2

Total area= 327 cm2

Have a great day