Use the Pythagorean theorem to calculate the length of the slope. This theorem states that the square of the height of the hill plus the square of the base of the hill is equal to the square of the length of the hill -- or in mathematical terms, a^2 + b^2 = c^2.
Use the variable "a" in the equation in Step 1 to represent the height of the hill. This measurement can be found on many maps, and is often measured in feet above sea level. So if the peak of the hill is 300 feet above sea level, and the bottom of the hill is 100 feet above sea level, then "a" is 200 feet. The square of this (a^2) is 40,000.
Use the variable "b" in the equation in Step 1 to represent the length of the base of the hill. This measurement can also be found on many maps. If you draw a vertical line from the peak of the hill vertically to the base, and draw a horizontal line from that point to the bottom of the hill where that line intersects with the slope, that measurement would be the base. For the purpose of this equation, we'll assume the base (b) is 800 feet. The square of that (b^2) is 640,000.
Add a^2 (40,000) to b^2 (640,000). That gives you 680,000. Remember in the original equation that the sum of a^2 + b^2 = c^2. This means that 680,000 is equal to c^2.
Take the square root of 680,000 to determine the value of "c." The square root of 680,000 is 824.6, rounding to the first decimal place. Therefore, the length of the slope of the hill is just under 825 feet.
Use the height and the grade of the hill to calculate the length of the slope. Use the equation (H/L) x 100 = G (where "G" is the variable for the grade).
Find out the grade of the hill, the variable "G" in the above equation. You can sometimes find this information on road signs; a sign might be posted to warn truckers of a "5 percent grade" ahead. You may also be able to obtain this information by contacting your state's department of transportation or even a team of surveyors. For this equation, we'll say this is a 5 percent grade, making the variable G = 5.
Measure the height -- the variable "H" in the above equation -- of the hill. This is the difference in the altitude of the peak of the hill from the altitude at the hill's base. So if the hill's peak is 300 feet above sea level and its base is 100 feet above sea level, the different, or "H," is 200 feet.
Fill in the parts of the equation you already know: the variables "G" and "H." That gives us (200/L) x 100 = 5.
Even out the equation by dividing both sides by 100. That gives us 200/L = 5/100. This equation now shows us that two fractions are equal in value. To determine the value of "L," multiply the top number in one fraction by the bottom number in the other. That gives us 5 x L = 200 x 100, or simplified, 5 x L = 20,000.
Isolate the variable "L" by dividing both sides by 5. That gives us L = 20,000/5, or simplified, L = 4,000. Therefore, the length of the slope of the hill is 4,000 feet.