Introduction:
Trapezoid is quadrilateral with pair of non parallel sides and other two sides are parallel.The parallel sides of trapezoid is known as bases.If two sides which are not parallel to each other have equal lengths, then trapezoid is called an isosceles trapezoid.Base angles in this trapezoid are equal in measurement.Height of a trapezoid is valuable to find the area of a trapezoid.
Formula:
Height of trapezoid is the perpendicular distance between the bases.
Therefore formula for finding height given as,
height of trapezoid = 2 area / (sum of bases)
Problems:
Problem 1:
Compute height of an isosceles trapezoid with sides of lengths 4, 7, 7 and 10.
Solution:
With bases of 4 and 10, longer base extends 3 more on each side. To find trapezoid's height,
a² + 3² = 7²
a² + 9 = 49
a² = 40
a = 6.3245
Problem 2:
How do you find the height of trapezoid or isosceles trapezoid?
Given legs=25 (isosceles) base=50 top=24.
Solution:
Base is 50 and the top is 24.
Find left of the base corresponding to the triangle, take 50 - 24 and get 26.
26 divide it by 2 and get 13.
You now have a triangle with base of 13 and hypotenuse of 25.
Pythagorean Theorem to find height of triangle, which will be the height of trapezoid.
13^2 + b^2 = 25^2
b^2 = 456
b = 21
Height of trapezoid is 21.
Problem 3:
Imagine trapezoid ABCD with AD parallel to BC has angle D equal to 40 degrees, Length of DC equal to 2 meters, length of BC equal to 5 meters and area of trapezoid is equal to 20 m 2. Calculate length of AD.
Solution:
Use definition of sine in right triangle to find the height h of trapezoid.
sin D = h / CD
Work out the above for h.
h = CD * sin D = 2 * sin 40
Formula of the area should be used to obtain the following equation.
area of trapezoid ABCD = 0.5 * h * (BC + AD)
Above equation has only one unknown: AD. Substitute all the known quantities to obtain
20 = 0.5 * 2 * sin 40 *(5 + AD)
Solve for AD.
AD = 20 / (0.5*2*SIN 40) - 5 = 26.11 meters (approximated to two decimal places).
Trapezoid is quadrilateral with pair of non parallel sides and other two sides are parallel.The parallel sides of trapezoid is known as bases.If two sides which are not parallel to each other have equal lengths, then trapezoid is called an isosceles trapezoid.Base angles in this trapezoid are equal in measurement.Height of a trapezoid is valuable to find the area of a trapezoid.
Formula:
Height of trapezoid is the perpendicular distance between the bases.
Therefore formula for finding height given as,
height of trapezoid = 2 area / (sum of bases)
Problems:
Problem 1:
Compute height of an isosceles trapezoid with sides of lengths 4, 7, 7 and 10.
Solution:
With bases of 4 and 10, longer base extends 3 more on each side. To find trapezoid's height,
a² + 3² = 7²
a² + 9 = 49
a² = 40
a = 6.3245
Problem 2:
How do you find the height of trapezoid or isosceles trapezoid?
Given legs=25 (isosceles) base=50 top=24.
Solution:
Base is 50 and the top is 24.
Find left of the base corresponding to the triangle, take 50 - 24 and get 26.
26 divide it by 2 and get 13.
You now have a triangle with base of 13 and hypotenuse of 25.
Pythagorean Theorem to find height of triangle, which will be the height of trapezoid.
13^2 + b^2 = 25^2
b^2 = 456
b = 21
Height of trapezoid is 21.
Problem 3:
Imagine trapezoid ABCD with AD parallel to BC has angle D equal to 40 degrees, Length of DC equal to 2 meters, length of BC equal to 5 meters and area of trapezoid is equal to 20 m 2. Calculate length of AD.
Solution:
Use definition of sine in right triangle to find the height h of trapezoid.
sin D = h / CD
Work out the above for h.
h = CD * sin D = 2 * sin 40
Formula of the area should be used to obtain the following equation.
area of trapezoid ABCD = 0.5 * h * (BC + AD)
Above equation has only one unknown: AD. Substitute all the known quantities to obtain
20 = 0.5 * 2 * sin 40 *(5 + AD)
Solve for AD.
AD = 20 / (0.5*2*SIN 40) - 5 = 26.11 meters (approximated to two decimal places).
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