The two legs of a right triangle can serve as its base and its height. The area of the triangle is half the product of the two:

$\displaystyle \frac{1}{2} \cdot 50 \cdot 120 = 3,000$

That is, the area is 3,000 square millimeters.

The area of a triangle is one half the product of its base and its height - in the above diagram, that means

$\displaystyle A = \frac{1}{2}xy$.

Substitute $\displaystyle A = 450, x = 20$, and solve for $\displaystyle y$ :

$\displaystyle \frac{1}{2} \cdot 20 \cdot y = 450$

$\displaystyle 10 \cdot y = 450$

$\displaystyle 10 \cdot y \div 10 = 450 \div 10$

$\displaystyle y = 45 \textrm{ cm}$

To find the area of a triangle, multiply the base of the triangle by the height and then divide by two.

$\displaystyle 10*12=120$ 

$\displaystyle 120/2=60$

The area of the entire square is the square of the length of a side, or

$\displaystyle 80 \times 80 = 6,400$.

The area of the white right triangle is half the product of its legs, or

$\displaystyle \frac{1}{2} \times 30 \times 60 = 900$.

Therefore, the area of that triangle is 

$\displaystyle \frac{900 }{6,400} \times 100 = 14 \frac{1}{16} \%$

of that of the entire square.

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

$\displaystyle \frac{1}{2} \times 140 \times 160 = 11,200$ square meters.

The portion he sold his brother, represented by the red right triangle, has area

$\displaystyle \frac{1}{2} \times 56 \times 128 = 3,584$ square meters.

Therefore, the area of the parcel Mr. Jones retained is 

$\displaystyle 11,200 -3,584= 7,616$ square meters.

From this shape we are able to see that we have a square and a triangle, so lets split it into the two shapes to solve the problem. We know we have a square based on the 90 degree angles placed in the four corners of our quadrilateral. 

Since we know the first part of our shape is a square, to find the area of the square we just need to take the length and multiply it by the width. Squares have equilateral sides so we just take 5 times 5, which gives us 25 inches squared.

We now know the area of the square portion of our shape. Next we need to find the area of our right triangle. Since we know that the shape below the triangle is square, we are able to know the base of the triangle as being 5 inches, because that base is a part of the square's side. 

To find the area of the triangle we must take the base, which in this case is 5 inches, and multipy it by the height, then divide by 2. The height is 3 inches, so 5 times 3 is 15. Then, 15 divided by 2 is 7.5. 

We now know both the area of the square and the triangle portions of our shape. The square is 25 inches squared and the triangle is 7.5 inches squared. All that is remaining is to added the areas to find the total area. Doing this gives us 32.5 inches squared. 

Area of a triangle can be determined using the equation:

$\displaystyle \small A=\frac{1}{2}bh$

$\displaystyle \small A=\frac{1}{2}(14)(5)=35$

The area of a right triangle is half the product of the lengths of its legs, so we need to use the Pythagorean Theorem to find the length of the other leg. Set $\displaystyle c = 25, b = 15$:

$\displaystyle a^{2} = c^{2} - b^{2}$

$\displaystyle a^{2} = 25^{2} - 15^{2}$

$\displaystyle a^{2} = 625-225$

$\displaystyle a^{2} =400$

$\displaystyle a = \sqrt{400} = 20$

The legs are 15 and 20 inches long. Divide both dimensions by 12 to convert from inches to feet:

$\displaystyle 20 \div 12 = \frac{5}{3}$ feet

$\displaystyle 15 \div 12 = \frac{5}{4}$ feet

Now find half their product:

$\displaystyle A = \frac{1}{2} \times \frac{5}{3}\times \frac{5}{4} = \frac{25}{24} = 1 \frac{1}{24}$ square feet

The area of the entire rectangle is the product of its length and width, or

$\displaystyle 120 \times 50 = 6,000$.

The area of the right triangle is half the product of its legs, or

$\displaystyle \frac{1}{2} \times 40 \times 80 = 1,600$

The area of the green region is therefore the difference of the two, or

$\displaystyle 6,000 - 1,600 = 4,400$.

The green region is therefore

$\displaystyle \frac{4,400}{6,000} \times 100 = 73 \frac{1}{3} \%$

of the rectangle.

The area of the entire rectangle is the product of its length and width, or

$\displaystyle 120 \times 50 = 6,000$.

The area of the right triangle is half the product of its legs, or

$\displaystyle \frac{1}{2} \times 40 \times 80 = 1,600$

The area of the green region is therefore the difference of the two, or

$\displaystyle 6,000 - 1,600 = 4,400$.

The ratio of the area of the green region to that of the white region is 

$\displaystyle \frac{4,400}{1,600} = \frac{4,400 \div 400}{1,600\div 400} = \frac{11}{4}$

That is, 11 to 4.