0
How do you calculate the area of anisosceles trapezoid if you only know the width of the base and the length and angle of the sides?
Danpotter
One way would be as follows:
Let b represent the length of the base, l the length of each of the two sides, and theta the angle between the base and the two sides of length l. Now drop a perpendicular line from each vertex at the top of the trapezoid to the base. This yields two right triangles and a rectangle in the middle. The height of each right triangle (as well as the height of the rectangle) equals l*sin(theta) [because sin(theta)=opposite/hypotenuse] and the length of the base of each right triangle is l*cos(theta). The base of the rectangle is b minus the lengths of the two right triangles.
Area of the trapezoid=2*area of each right triangle+area of the rectangle=2*(1/2)*(l*sin(theta)*l*cos(theta))+(b-2*l*cos(theta))(l*sin(theta))=)*(l*sin(theta)*l*cos(theta))+(b-2*l*cos(theta))(l*sin(theta))=b*l*sin(theta)-l2*sin(theta)*cos(theta)
Wiki User
∙ 14y ago
Add your answer:
Earn +20 pts
What a trapezoid with only 1 right angle?
a right trapezoid
How do you calculate the angles of an isosceles trapezoid?
Two angles must be equal and when added to the third angle should total 180 degrees.
How do you calculate 45 degree area?
The 45 degrees is an angle. To calculate an area the length and width are needed.
How do you use sine in math?
The sine function is used in trigonometric calculations when attempting to find missing side lengths of a right triangle. The sine of an angle in a triangle is equal to the length of the side opposite of that angle divided by the length of the hypotenuse of the triangle. Using this fact you can calculate the length of the hypotenuse if you know an angle measure and the length of one leg of the triangle. You can also calculate the length of a leg of the triangle if you know an angle measure and the length of the hypotenuse.
If the length of the bases of an isosceles trapezoid are known can you compute the measure of the internal angles?
Let's do an example.Draw an isosceles trapezoid. Let say that the biggest base has a length of 10, and the smallest base has a length of 4.Draw two perpendicular line that pass through the vertices of the smallest base, to the biggest base of the trapezoid.A rectangle is formed whose lengths of its two opposite sides equal to the length of the smallest base of the trapezoid.Then, we can say that the base of the right triangle whose hypotenuse is one one of the congruent sides of the trapezoid is 3, (1/2)(10 -4). So that one of the possibilities of its height (which also is the height of the trapezoid) is 4, and the hypotenuse is 5 (by the Pythagorean triple).Now, in the right triangle whose hypotenuse is one of the congruent sides of the trapezoid, we have:tan (base angle of the trapezoid) = 4/3, andthe base angle angle of the trapezoid = tan-1 (4/3) ≈ 53⁰.Since the sum of the two adjacent angles of the trapezoid is 180⁰, the other angle of the trapezoid is 127⁰.Thus, the base angles of the isosceles trapezoid have a measure of 53⁰, and two other angles have a measure of 127⁰.So, we need to have more information in order to find the angles of the isosceles trapezoid for the given problem.
How do you draw a trapezoid?
Draw two parallel lines of unequal length, and connect their end points. If you have a right angle, it is a right trapezoid. If the non-parallel sides are equal in length, it is an isosceles trapezoid.
How do you calculate tangent of an angle?
the tangent of an angle is equal to the length of the opposite side from the angle divided by the length of the side adjacent to the angle.
Which figure has 2 right angle 1 obtuse angle and 1 acute angle?
It fits the description of a trapezoid
How do you calculate the the arc of a sector?
To calculate the arc length of a sector: calculate the circumference length, using (pi * diameter), then multiply by (sector angle / 360 degrees) so : (pi * diameter) * (sector angle / 360) = arc length
What a trapezoid with only 1 right angle?
a right trapezoid
How do you calculate the angles of an isosceles trapezoid?
Two angles must be equal and when added to the third angle should total 180 degrees.
How do you calculate 45 degree area?
The 45 degrees is an angle. To calculate an area the length and width are needed.
How do you use sine in math?
The sine function is used in trigonometric calculations when attempting to find missing side lengths of a right triangle. The sine of an angle in a triangle is equal to the length of the side opposite of that angle divided by the length of the hypotenuse of the triangle. Using this fact you can calculate the length of the hypotenuse if you know an angle measure and the length of one leg of the triangle. You can also calculate the length of a leg of the triangle if you know an angle measure and the length of the hypotenuse.
If the length of the bases of an isosceles trapezoid are known can you compute the measure of the internal angles?
Let's do an example.Draw an isosceles trapezoid. Let say that the biggest base has a length of 10, and the smallest base has a length of 4.Draw two perpendicular line that pass through the vertices of the smallest base, to the biggest base of the trapezoid.A rectangle is formed whose lengths of its two opposite sides equal to the length of the smallest base of the trapezoid.Then, we can say that the base of the right triangle whose hypotenuse is one one of the congruent sides of the trapezoid is 3, (1/2)(10 -4). So that one of the possibilities of its height (which also is the height of the trapezoid) is 4, and the hypotenuse is 5 (by the Pythagorean triple).Now, in the right triangle whose hypotenuse is one of the congruent sides of the trapezoid, we have:tan (base angle of the trapezoid) = 4/3, andthe base angle angle of the trapezoid = tan-1 (4/3) ≈ 53⁰.Since the sum of the two adjacent angles of the trapezoid is 180⁰, the other angle of the trapezoid is 127⁰.Thus, the base angles of the isosceles trapezoid have a measure of 53⁰, and two other angles have a measure of 127⁰.So, we need to have more information in order to find the angles of the isosceles trapezoid for the given problem.
Can a trapezoid have one right angle?
it doesn't normally but it can and still be a trapezoid
What is the formula to calculate the length of a chord given the included angle and radius?
the length is: 2rsin(1/2 theta) where r is the radius and theta is the included angle.
How do you calculate the angle for length 2700 and height 1680?
Using these two measurements you would calculate the angle using the tangent. In this case: tan (theta) = 1680/2700
