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.