the formula for the area of a trapezoid is a=1/2h(b1+b2). which equations area of a trapezoid is a=1/2h(b1+b2). which equations are equivalent to the formula? h=2a/b1+b2, B1=2a/h-b2, b2=2a/b1-h, b2=2a/h-b1, or b1-2a/b2-h?
what’s the answer ?
The answer is b1=2A/h-b2;b1=6 meters
Answer is simple. Imagine x/5+2 if you wanted to put the 2 in the fraction, you would put it in the numerator and multiply "2" by the value in the denominator. So you would get (x+2(5))/5 --> x+10/5
Same logic applies here. Take b(2) in the equation "b1 = 2A/h-b2" and then put it in the numerator and multiply by the denominator which is 2A-b2*h/h which is the final answer 😌👍
69
To determine which equations are equivalent to the formula for the area of a trapezoid, we can substitute the given formula into each of the options and simplify to see if they match.
Given formula for the area of a trapezoid:
A = (1/2)h(b1 + b2)
Option 1: h = 2a/(b1 + b2)
Substituting the given formula:
A = (1/2)(2a/(b1 + b2))(b1 + b2)
A = a
Option 2: B1 = 2a/h - b2
Substituting the given formula:
A = (1/2)h((2a/h - b2) + b2)
A = (1/2)h(2a/h)
A = a
Option 3: b2 = 2a/(b1 - h)
Substituting the given formula:
A = (1/2)h(b1 + (2a/(b1 - h)))
A = (1/2)h(b1(b1 - h) + 2a)/(b1 - h)
Expanding the numerator:
A = (1/2)h(b1^2 - b1h + 2a)/(b1 - h)
This equation is not equivalent to the original formula.
Option 4: b2 = 2a/h - b1
Substituting the given formula:
A = (1/2)h(b1 + (2a/h - b1))
A = (1/2)h(2a/h)
A = a
Option 5: b1 - 2a/b2 - h
Substituting the given formula:
A = (1/2)h((b1 - 2a)/(b2 - h) + b2)
The numerator is not equivalent to the original formula.
Therefore, the equations that are equivalent to the formula for the area of a trapezoid are:
- h = 2a / (b1 + b2)
- B1 = 2a / h - b2
- b2 = 2a / h - b1
Please note that the option given in your question, b2 = 2a / b1 - h, is not equivalent to the formula for the area of a trapezoid.
well, you can start by noting that
a = 1/2 h (b1+b2)
is the same as
hb1 + hb2 = 2a
Now solve for b1 or b2 and see which formula you want.