Question

22. Find the perimeter and area.

24. Find the perimeter and area.

26. Find the area of the figure.

Answer 1

Part 22) The area is
`A=15a^3b^6\ units^2(` and the perimeter is
`P=10a^2b^4+6ab^2\ unit`

Part 24) The area is
`A=16m^3n\ units^2` and the perimeter is
`P=24mn\ units`

Part 26) The area is equal to
`A=9\pi x^6y^(2)\ units^2`

Explanation:

Part 22) Find the perimeter and area

step 1

The area of a rectangle is equal to

`A=LW`

we have

`L=5(a^2)(b^4)\ units`

`W=3(a)(b^2)\ units`

Remember that

When multiply exponents with the same base, adds the exponents and maintain the base

substitute in the formula

`A=(5(a^2)(b^4))(3(a)(b^2))`

`A=15a^3b^6\ units^2`

step 2

The perimeter of a rectangle is equal to

`P=2(L+W)`

we have

`L=5(a^2)(b^4)\ units`

`W=3(a)(b^2)\ units`

substitute in the formula

`P=2(5(a^2)(b^4)+3(a)(b^2))`

`P=10a^2b^4+6ab^2\ unit`

Part 24) Find the perimeter and area

step 1

The area of triangle is equal to

`A=(1)/(2)bh`

where

`b=8mn\ units`

`h=4m^2\ units`

Remember that

When multiply exponents with the same base, adds the exponents and maintain the base

substitute the given values

`A=(1)/(2)(8mn)(4m^2)`

`A=16m^3n\ units^2`

step 2

Find the perimeter

I will assume that is an equilateral triangle (has three equal length sides)

The perimeter of an equilateral triangle is

`P=3b`

where

`b=8mn\ units`

substitute

`P=3(8mn)`

`P=24mn\ units`

Part 26) Find the area

The area of a circle is equal to

`A=\pi r^(2)`

where

`r=3x^3y\ units`

Remember the property

`(a^(m))^(n)=a^(m*n)`

substitute in the formula the given value

`A=\pi (3x^3y)^(2)`

`A=9\pi x^6y^(2)\ units^2`