Trouble with a polygon!

[kayleyrae]

I'm sure this problem ought to be very simple, but it's proved difficult for me:

I plugged the formula (152 = a+20/2 * 8) into the geometry helper on freemathhelp out of desperation, and came up with a=18.
HOW did they get from the formula to the answer? By what process? Please help and thank you!!

 

[Deleted member 4993]

I'm sure this problem ought to be very simple, but it's proved difficult for me:

I plugged the formula (152 = a+20/2 * 8) into the geometry helper on freemathhelp out of desperation, and came up with a=18.
HOW did they get from the formula to the answer? By what process? Please help and thank you!!

Do you know the name of the shape you are investigating?

 

[pka]

I'm sure this problem ought to be very simple, but it's proved difficult for me:
I plugged the formula (152 = a+20/2 * 8) into the geometry helper on freemathhelp out of desperation, and came up with a=18.
HOW did they get from the formula to the answer? By what process? Please help and thank you!!

The area of a trapezoid is the average of the bases times the height.

\(\displaystyle 8\cdot \dfrac{x+20}{2}\)

 

[HallsofIvy]

That looks exactly like the kind of problem you would get just after learning the formula for the area of a trapezoid. A trapezoid is a lot like a rectangle except that two sides are parallel but not of the same length. You have to use the average of the two lengths, \(\displaystyle \frac{b_1+ b_2}{2}\), so that the area is \(\displaystyle h\frac{b_1+ b_2}{2}\). Here, the bases are 20 and x and "h" is 8: so \(\displaystyle 8\left(\frac{20+ x}{2}\right)= 152\). Solve that for x.

 

[Quaid]

152 = (a+20)/2 * 8

the geometry helper came up with a=18.

HOW did they get from the formula to the answer? By what process?

Hi Kay:

First, a note about notation. You must include grouping symbols around the numerator (as shown in red above), when typing it; they aren't needed, when handwritten.

We "solve the equation 152=(a+20)/2*8 for a", and the result is a=18.

This solving-process is called algebra.

Here are the steps, to solve the equation for a.

1) Simplify the right-hand side to 4(a+20)

2) Divide each side by 4

3) Subtract 20 from each side

Questions?

 

[HallsofIvy]

Actually, I would go further and say that the original equation should be written ((x+ 20)/2)8 since if you write just (x+ 20)/2*8, some might think the 8 was in the denominator.

 

[Quaid]

some might think the 8 was in the denominator

Bless their heart!