Answer:
Area: [tex]17a^2b[/tex]
Perimeter: [tex]P = 10a^2+10b[/tex]
Step-by-step explanation:
Area
The area of the entire rectangle that is 4b by [tex]a^2+3a^2+a^2 = 5a^2[/tex] is found using A = l*w. If w=4b and l=[tex]5a^2[/tex] then the area is:
[tex]A=l*w\\A=5a^2(4b)\\A=20a^2b[/tex]
However there is a cutout in the middle. Find the area of the cut out and subtract from the total area.
The cutout is [tex]3a^2[/tex] by b. So the area is:
[tex]A=l*w\\A=3a^2*b\\A=3a^2b[/tex]
Subtract [tex]20a^2b - 3a^2b = 17a^2b[/tex]
Perimeter
The perimeter is the distance around the entire figure. To find it, add each side length. Then add like terms together.
[tex]P = a^2 +b + 3a^2 + b +a^2+4b+5a^2+4b\\P = 10a^2+10b[/tex]
