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

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 9cm.  Because it is a rectangle, the opposite side is also 9cm.

We can see the width is 7cm.  Because it is a rectangle, the opposite side is also 7cm.

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

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

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

Now, we know the width of the rectangle is 6in.  Because it is a rectangle, the opposite side is also 6in.

We know the length is three times the width.  Therefore, the length is 18in.  Because it is a rectangle, the opposite side is also 18in.

So, we can substitute.  We get

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

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

Now, we know the width of the rectangle is 4cm.  Because it is a rectangle, the opposite side is also 4cm. 

We know the length is three times the width.  Therefore, the length is 12cm.  Because it is a rectangle, the opposite side is also 12cm.  

So, we can substitute. 

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

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

Now, we know the width of the rectangle is 6in.  Because it is a rectangle, the opposite side is also 6in.  

We know the length is two times the width.  Therefore, the length is 12in.  Because it is a rectangle, the opposite side is also 12in. 

So, we get

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

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

Now, we know the length of the rectangle is 16cm.  Because it is a rectangle, the opposite side is also 16cm.  We also know the width of the rectangle is a quarter of the length.  To find the width, we will divide 16 by 4.  Therefore, the width is 4cm.  Because it is a rectangle, the opposite side is also 4cm.

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

This problem requires finding the height of the rectangle first.

Write the formula for the area of the rectangle, and substitute the known values.

Divide by two on both sides to obtain the height.

The perimeter of a rectangle includes 2 bases and 2 heights.

The formula for the perimeter is:

Substitute the values to find the perimeter.

The perimeter is:  

To find the area of a trapezoid, multiply one half (or 0.5, since we are working with decimals) by the sum of the lengths of its bases (the parallel sides) by its height (the perpendicular distance between the bases). This quantity is

The area of a trapezoid can be determined using the equation .

To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.

The length of a leg of  is equal to the height of the orange region, which is a trapezoid. Call this length/height .

Since the triangle is isosceles, then , and since  is the midpoint of , . Also, since opposite sides of a rectangle are congruent, 

Therefore, the orange region is a trapezoid with bases  and  and height . Its area is 72, so we can set up and solve this equation using the area formula for a trapezoid:

This is the length of one leg of the triangle.