The perimeter of square \(\displaystyle ABCD\) can be found by applying the formula: 

\(\displaystyle 4S\), where \(\displaystyle S=\) the length of one side of the square.

To find the length of the square look at the coordinates:

\(\displaystyle A=(0,0), B=(5,0)\rightarrow S=5\)

Thus, 
\(\displaystyle S=5\)
\(\displaystyle p=4\times5=20\)

If the points are plotted on to a graph, you should notice that the points form a square with side lengths of \(\displaystyle 2\).

The area of a trapezoid is given by the formula \(\displaystyle \frac{1}{2} *height* (base_{long} + base_{short})\).

We know that the height is 1, the long base is 4, and the short base is 2.

\(\displaystyle \frac{1}{2} *height* (base_{long} + base_{short})=\frac{1}{2} *(1)* ((4) + (2))\)

\(\displaystyle \frac{1}{2}*(6)\)

\(\displaystyle 3\)

The find the area of a trapezoid, use:

\(\displaystyle area=\left ( \frac{b1+b2}{2} \right )\times h\)

The area of the yard is the area of the small trapezoid subtracted from that of the large rectangle. The area of a rectangle is the product of its length and its height, so the large rectangle has area

\(\displaystyle 105 \times 85 = 8,925\) square meters. 

The area of a trapezoid is half the product of its height and the sum of its two parallel sides (bases), so the small trapezoid has area

\(\displaystyle \frac{1}{2} \times 40 \times (30 + 40) = \frac{1}{2} \times 40 \times 70 = 1,400\) square meters.

The area of the yard is the difference of the two:

\(\displaystyle 8,925- 1,400 = 7,525\) square meters.

The area of a triangle is half the product of its base and its height, so Mr. Smith's parcel originally had area 

\(\displaystyle \frac{1}{2 } \times 200 \times 250 = 25,000\) square feet.

The area of a trapezoid is the half product of its height and the sum of its two parallel sides (bases), so the portion Mr. Smith sold to his brother has area

\(\displaystyle \frac{1}{2} \times 50 \times (80 + 100) = 4,500\) square feet.

Therefore, Mr. Smith retains a parcel of area

\(\displaystyle 25,000 - 4,500 = 20,500\) square feet.

The formula for the area of a trapezoid is \(\displaystyle \frac{base_1 + base_2}{2}\cdot height\)

In other words, find the average of the bases and multiply by the height. Substituting in the values of the bases for the given trapezoid, \(\displaystyle 9\) and \(\displaystyle 7\), you get:

 \(\displaystyle \frac{9\:in+7\:in}{2}\cdot 5\:in = 8\:in\cdot 5\:in=40\:in^2\)

The formula for the area of a trapezoid is \(\displaystyle \frac{base_1 + base_2}{2}\cdot height\)

In other words, find the average of the bases and multiply by the height. Substituting the values of the bases of the given trapezoid, \(\displaystyle 8\:cm\) and \(\displaystyle 12\:cm\), into the equation, you get:

\(\displaystyle \frac{8\:cm+12\:cm}{2}\cdot 5\:cm = 10\:cm\cdot 5\:cm=50\:cm^2\)

The area of the trapezoid is thus \(\displaystyle 50\:cm^2\).

In order to find the perimeter of the trapezoid, we have to add up all the outer sides:

\(\displaystyle 6+3+5+7=21\)

In order to find the perimeter we must add up all the outer sides of the trapezoid.

\(\displaystyle 5+9+7+8=29\)