Question

Find the area and perimeter.
The area is ... and the perimeter is ...

Answer 1

Area:
`17a^2b`

Perimeter:
`P = 10a^2+10b`

Explanation:

Area

The area of the entire rectangle that is 4b by
`a^2+3a^2+a^2 = 5a^2` is found using A = l*w. If w=4b and l=
`5a^2` then the area is:

`A=l*w\\A=5a^2(4b)\\A=20a^2b`

However there is a cutout in the middle. Find the area of the cut out and subtract from the total area.

The cutout is
`3a^2` by b. So the area is:

`A=l*w\\A=3a^2*b\\A=3a^2b`

Subtract
`20a^2b - 3a^2b = 17a^2b`

Perimeter

The perimeter is the distance around the entire figure. To find it, add each side length. Then add like terms together.

`P = a^2 +b + 3a^2 + b +a^2+4b+5a^2+4b\\P = 10a^2+10b`