To find the perimeter of a rectangle, you must first understand that a rectangle's opposite sides are equal. Therefore if you know the length of one side it is the identical length of the opposite side.

$\displaystyle 12cm + 12cm = 24cm$

$\displaystyle 4cm +4cm=8cm$

$\displaystyle 24cm+8cm=32cm$

32cm is your answer.

First you need to understand that opposite sides of a rectangle are equal. Then you are able to add the value of each side to itself and then add your sums together to get the perimeter of a rectangle.

$\displaystyle 10cm+10cm=20cm$

$\displaystyle 7cm+7cm=14cm$

$\displaystyle 20cm+14cm=34cm$

To find the perimeter of a rectangle, we will use the following formula:

$\displaystyle \text{perimeter of rectangle} = a+b+c+d$

Where a, b, c, and d are the lengths of the sides of the rectangle.

Now, let's look at the rectangle.

We can see the length is 6in.  Because it is a rectangle, the opposite side is also 6in. 

We can also see the width of the rectangle is 3in. Because it is a rectangle, the opposite side is also 3in.

Knowing this, we can substitute into the formula.  We get

$\displaystyle \text{perimeter of rectangle} = 6\text{in} + 6\text{in} + 3\text{in} + 3\text{in}$

$\displaystyle \text{perimeter of rectangle} = 18\text{in}$

To find the perimeter of a rectangle, we will use the following formula:

$\displaystyle P = a+b+c+d$

Where a, b, c, and d are the lengths of the sides of the rectangle.

Now, given the rectangle

we can see the length is 11in.  Because it is a rectangle, the opposite side is also 11in.

The width is 5in.  Because it is a rectangle, the opposite side is also 5in.

So, we can substitute.

$\displaystyle P = 11\text{in} + 11\text{in} + 5\text{in} + 5\text{in}$

$\displaystyle P = 32\text{in}$

The formula for perimeter of a rectangle is $\displaystyle P=2(l + w)$

To solve for the width we can plug our known values into the equation. 

$\displaystyle 10=2(2+w)$

$\displaystyle 10=4+2w$

Subtract $\displaystyle 4$ from both sides

$\displaystyle 6=2w$

Divide $\displaystyle 2$ by both sides

$\displaystyle 3=w$

$\displaystyle P=2l+ 2w$

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

$\displaystyle 54=2l+2(17)$

$\displaystyle 54=2l+34$

Subtract $\displaystyle 34$ from both sides

$\displaystyle 54-34=2l+34-34$

$\displaystyle 20=2l$

Divide $\displaystyle 2$ by both sides

$\displaystyle \frac{20}{2}=\frac{2l}{2}$

$\displaystyle 10=l$

The formula for perimeter of a rectangle is $\displaystyle P=2(l + w)$

To solve for the perimeter we can plug our known values into the equation. 

$\displaystyle P=2(7+4)$

$\displaystyle P=2(11)$

$\displaystyle P=22$

The fence is going around the garden, so this is a perimeter problem. 

$\displaystyle P=2l+2w$

$\displaystyle P=2(6)+2(3)$

$\displaystyle P=12+6$

$\displaystyle P=18$

The fence is going around the backyard, so this is a perimeter problem. 

$\displaystyle P=2l+2w$

$\displaystyle P=2(5)+2(4)$

$\displaystyle P=10+8$

$\displaystyle P=18$

The area of a triangle is given by $\displaystyle 0.5\times altitude\times base$.

altitude $\displaystyle = 10$

base $\displaystyle = 3\times a$ = $\displaystyle 30$

Therefore:

Area $\displaystyle = 0.5\times10\times30 = 150$