Fomula: A=1/2(b1+b2)h
A=area of a trapezoid
b1=width at the top
b2-width at the bottom
h=height
A 7-foor tall trapezoid has 42 square feet of area. If is is 9 feet wide at the bottom, how far across is it at the top?
I will set it up for you and you can simplify.
A = 42
h = 7
b2 = 9
I will plug and you can chug.
42 = 1/2(b1 + 9)(7)
Solve for b1, which is read "b sub one."
Can you take it from here?
Thank you for your response. I can set up and calculate. The book says I should be getting 3 feet as my answer. That is not what I am getting.
Here it is:
First multiply 7 x 1/2 = 7/2.
We now have this equation:
42 = 7/2(b1) + 9)
Simplify the right side of the equation and the whole thing becomes
42 = 7/2(b1) + 63/2
Subtract 63/2 from 42.
42 - 63/2 = 10_1/2
We now have:
10_1/2 = 7/2(b1)
10_1/2 divided by 7/2 = b1
3 feet = b1
Done!
To find the width at the top of the trapezoid, we can rearrange the formula:
A = 1/2(b1 + b2)h
First, let's substitute the given values into the formula:
A = 42 square feet
b1 = ?
b2 = 9 feet
h = 7 feet
42 = 1/2(b1 + 9) * 7
Now, we can solve for b1 by isolating the variable on one side of the equation. Multiply both sides of the equation by 2 to get rid of the fraction:
42 * 2 = (b1 + 9) * 7
84 = 7(b1 + 9)
Next, distribute the 7 to both terms inside the parentheses:
84 = 7b1 + 63
Subtract 63 from both sides of the equation:
84 - 63 = 7b1
21 = 7b1
Finally, divide both sides of the equation by 7 to solve for b1:
21/7 = b1
b1 = 3
Therefore, the width at the top of the trapezoid is 3 feet.