Answer:
Part 22) The area is [tex]A=15a^3b^6\ units^2([/tex] and the perimeter is [tex]P=10a^2b^4+6ab^2\ unit[/tex]
Part 24) The area is [tex]A=16m^3n\ units^2[/tex] and the perimeter is [tex]P=24mn\ units[/tex]
Part 26) The area is equal to [tex]A=9\pi x^6y^{2}\ units^2[/tex]
Step-by-step explanation:
Part 22) Find the perimeter and area
step 1
The area of a rectangle is equal to
[tex]A=LW[/tex]
we have
[tex]L=5(a^2)(b^4)\ units[/tex]
[tex]W=3(a)(b^2)\ units[/tex]
Remember that
When multiply exponents with the same base, adds the exponents and maintain the base
substitute in the formula
[tex]A=(5(a^2)(b^4))(3(a)(b^2))[/tex]
[tex]A=15a^3b^6\ units^2[/tex]
step 2
The perimeter of a rectangle is equal to
[tex]P=2(L+W)[/tex]
we have
[tex]L=5(a^2)(b^4)\ units[/tex]
[tex]W=3(a)(b^2)\ units[/tex]
substitute in the formula
[tex]P=2(5(a^2)(b^4)+3(a)(b^2))[/tex]
[tex]P=10a^2b^4+6ab^2\ unit[/tex]
Part 24) Find the perimeter and area
step 1
The area of triangle is equal to
[tex]A=\frac{1}{2}bh[/tex]
where
[tex]b=8mn\ units[/tex]
[tex]h=4m^2\ units[/tex]
Remember that
When multiply exponents with the same base, adds the exponents and maintain the base
substitute the given values
[tex]A=\frac{1}{2}(8mn)(4m^2)[/tex]
[tex]A=16m^3n\ units^2[/tex]
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
[tex]P=3b[/tex]
where
[tex]b=8mn\ units[/tex]
substitute
[tex]P=3(8mn)[/tex]
[tex]P=24mn\ units[/tex]
Part 26) Find the area
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
where
[tex]r=3x^3y\ units[/tex]
Remember the property
[tex](a^{m})^{n}=a^{m*n}[/tex]
substitute in the formula the given value
[tex]A=\pi (3x^3y)^{2}[/tex]
[tex]A=9\pi x^6y^{2}\ units^2[/tex]
