You will need
- calculator
Instruction
1
In problems of geometry, more precisely on plane geometry and trigonometry, it is sometimes necessary to find the height of a parallelogram based on the given values of the sides, angles, diagonals, etc.
To find the altitude of a parallelogram, knowing its area and the length of the base, you must use the rule determining the area of the parallelogram. The area of a parallelogram, as is known, is equal to the product of the height to the length of the base:
S=a*h, where:
S - area of a parallelogram,
a - the base length of a parallelogram
h - length is omitted on the side and the height (or its continuation).
This implies that the height of the parallelogram will be equal to the area divided by the length of the base:
h=S/a
For example,
given: the area of a parallelogram is equal to 50 sq cm, base 10 cm;
find: the height of the parallelogram.
h=50/10=5 (cm).
To find the altitude of a parallelogram, knowing its area and the length of the base, you must use the rule determining the area of the parallelogram. The area of a parallelogram, as is known, is equal to the product of the height to the length of the base:
S=a*h, where:
S - area of a parallelogram,
a - the base length of a parallelogram
h - length is omitted on the side and the height (or its continuation).
This implies that the height of the parallelogram will be equal to the area divided by the length of the base:
h=S/a
For example,
given: the area of a parallelogram is equal to 50 sq cm, base 10 cm;
find: the height of the parallelogram.
h=50/10=5 (cm).
2
Because the height of the parallelogram side of the base and adjacent to the base side form a right triangle, to find the height of a parallelogram, you can use some ratios of sides and angles of right triangles.
If you know adjacent to the height h (DE) side d of the parallelogram (AD) and opposite to the elevation angle a (BAD) then calculate the height of a parallelogram multiply the length of the adjacent side to the sine of the opposite angle:
h=d*sinA,
for example, if d=10 cm and angle A=30 degrees,
H=10*sin(30º)=10*1/2=5 (cm).
If you know adjacent to the height h (DE) side d of the parallelogram (AD) and opposite to the elevation angle a (BAD) then calculate the height of a parallelogram multiply the length of the adjacent side to the sine of the opposite angle:
h=d*sinA,
for example, if d=10 cm and angle A=30 degrees,
H=10*sin(30º)=10*1/2=5 (cm).
3
If in terms of the problem specified length adjacent to the height h (DE) side d of the parallelogram (AD) and length intercept height of the base (AE), then the height of the parallelogram can be found using the Pythagorean theorem:
|AE|^2+|ED|^2=|AD|^2, where-defined:
h=|ED|=√(|AD|^2-|AE|^2),
i.e., the height of a parallelogram is equal to the square root of the difference of the squares of the lengths of the adjacent side and cut off the height of the base.
For example, if the length of the adjacent side is 5 cm, and the length of the intercept of the base is 3 cm, then length will be the height:
h=√(5^2-3^2)=4 (cm).
|AE|^2+|ED|^2=|AD|^2, where-defined:
h=|ED|=√(|AD|^2-|AE|^2),
i.e., the height of a parallelogram is equal to the square root of the difference of the squares of the lengths of the adjacent side and cut off the height of the base.
For example, if the length of the adjacent side is 5 cm, and the length of the intercept of the base is 3 cm, then length will be the height:
h=√(5^2-3^2)=4 (cm).
4
If you know the length to the height of the adjacent diagonal (DB) of the parallelogram and the length of the intercept height of the base (VE), then the height of the parallelogram can also be found using the Pythagorean theorem:
|VE|^2+|ED|^2=|BD|^2, where-defined:
h=|ED|=√(|BD|^2-|VE|^2),
i.e., the height of a parallelogram is equal to the square root of the difference of the squares of the lengths of the adjacent and diagonal intercept altitude (and diagonal) of the base.
For example, if the length of the adjacent side is 5 cm, and the length of the intercept of the base is 4 cm, then the length of the height will be:
h=√(5^2-4^2)=3 (cm).
|VE|^2+|ED|^2=|BD|^2, where-defined:
h=|ED|=√(|BD|^2-|VE|^2),
i.e., the height of a parallelogram is equal to the square root of the difference of the squares of the lengths of the adjacent and diagonal intercept altitude (and diagonal) of the base.
For example, if the length of the adjacent side is 5 cm, and the length of the intercept of the base is 4 cm, then the length of the height will be:
h=√(5^2-4^2)=3 (cm).