What is the area of an isosceles trapezoid, if the lengths of its bases are 16 cm and 30 cm and the diagonals are perpendicular to each other?
Answers
Call the point of intersection of the diagonals point X.
Each base is the hypotenuse of an isosceles right triangle whose sides are the diagonals and whose 90° angle is at X. The altitude of that triangle (⊥ distance to the base from X) is half the length of the hypotenuse. Then the height of the trapezoid is half the sum of the base lengths.
The area of the trapezoid is the product of the height and half the sum of the base lengths, hence is the square of half the sum of the base lengths.
... Area = ((16 cm +30 cm)/2)² = (23 cm)² = 529 cm²
Final answer:
The area of the given isosceles trapezoid is 345 square cm.
Explanation:
To solve this problem, we need to remember that the area (A) of a trapezoid is given by the formula A = 0.5 * (b1+b2) * h, where b1 and b2 are the lengths of the two bases and h is the height. When the diagonals of an isosceles trapezoid are perpendicular to each other, it can be divided into two right triangles with bases 7 cm and 16 cm (as 30-16=14 and 14/2=7) and height h. From here, we can calculate that the hypotenuse (diagonal) is equal to sqrt(7^2 + 16^2) = 17. Hence, it is a Pythagorean triple, meaning the height is 15 cm. Using the formula for the area of a trapezoid, we can now calculate the area to be 0.5 * (16+30) * 15 = 345 cm^2.
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Answers
The y-value for the E coordinate after the translation of the points will be 9.
What is translation?
The process of changing the location of the image on the coordinate system will be known as the translation.
A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that triangle, EFG with the coordinates E (-3,5), F(-3, 1), (1, 1) is translated as 2 units left and 4 units up.
E(-3,5) translated 2 units left would be (-5,5), then translated 4 units up would be (-5,9).
Therefore, the y-value for the E coordinate after the translation of the points will be 9.
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Answer:
the y value would be 9
full translation(-5,9)
Step-by-step explanation:
E(-3,5) translated 2 units left would be (-5,5), then translated 4 units up would be (-5,9)
Answers
Answer:
731.355
Step-by-step explanation:
875.230 - 143.875 = 731.355
apples rotten fresh
Answers
Answer:
111°
Step-by-step explanation:
By exterior angle theorem:
Answer:
x = 111
Step-by-step explanation:
180- 82 -29 is 69 and 180-69 is x which x is equal to 111
Answers
Answer:
(2/3, -9/2)or (2/3, 4 1/2)
Step-by-step explanation:
80
120
48
144
Answers
Answer:
144
Step-by-step explanation:
first digit of the code: only 2 and 4 are the only even numbers availible, so only 2 possibilities for the first digit.
2nd digit of code: 2,5,7,9,1 so 6 possibilities for the 2nd digit.
3rd digit of code: 2,5,7,9,1 so 6 possibilities for the 3rd digit.
4th digit of code: only 7 and 9 are greater tyhan 6 so only 2 possibilities for the 4th digit.
SO...
2 x 6 x 6 x 2 = 144
Answers
Answer:
Wavelengths of all possible photons are;
λ1 = 9.492 × 10^(-8) m
λ2 = 1.28 × 10^(-6) m
λ3 = 1.28 × 10^(-6) m
λ4 = 4.04 × 10^(-6) m
Step-by-step explanation:
We can calculate the wavelength of all the possible photons emitted by the electron during this transition using Rydeberg's equation.
It's given by;
1/λ = R(1/(n_f)² - 1/(n_i)²)
Where;
λ is wavelength
R is Rydberg's constant = 1.0974 × 10^(7) /m
n_f is the final energy level = 1,2,3,4
n_i is the initial energy level = 5
At n_f = 1,.we have;
1/λ = (1.0974 × 10^(7))(1/(1)² - 1/(5)²)
1/λ = 10535040
λ = 1/10535040
λ = 9.492 × 10^(-8) m
At n_f = 2,.we have;
1/λ = (1.0974 × 10^(7))(1/(2)² - 1/(5)²)
1/λ = (1.0974 × 10^(7))(0.21)
1/λ = 2304540
λ = 1/2304540
λ = 4.34 × 10^(-7) m
At n_f = 3, we have;
1/λ = (1.0974 × 10^(7))(1/(3)² - 1/(5)²)
1/λ = (1.0974 × 10^(7))(0.07111)
1/λ = 780373.3333333334
λ = 1/780373.3333333334
λ = 1.28 × 10^(-6) m
At n_f = 4, we have;
1/λ = (1.0974 × 10^(7))(1/(4)² - 1/(5)²)
1/λ = (1.0974 × 10^(7))(0.0225)
1/λ = 246915
λ = 1/246915
λ = 4.04 × 10^(-6) m