Here is the formula:
[tex]A=\frac{1}{2}(b1+b2)h[/tex]
The first thing you need to do to solve this question is see the information you are given.
You are given:
- Area of the trapezoid(86 cm)
- Base 1(12 cm)
- Height(8 cm)
Now that you know what information is given, you need to plug it into the formula.
Replace the variables used in the formula with the values you are given.
[tex]A=\frac{1}{2}(b1+b2)h \\ \\ 86=\frac{1}{2}(12+b2)8[/tex]
Now you need to do multiply everything in order to 'simpify it'. I'm goinf to change b1 into x; x is the value of b1.
[tex]86=\frac{1}{2}(12+b2)8 \rightarrow 86=(\frac{1}{2}(12+x))(8)[/tex]
Multiply everything in the parentheses, but first start with the first one(parenthesis).
[tex]86=(\frac{1}{2}(12+x))(8) \rightarrow 86= (6+0.5x)(8)[/tex]
You need to have only 1 number/variable on each side. That means you have to multiply the values in the two parentheses:
[tex](6+0.5x)(8) \rightarrow 4x+48[/tex]
Here is your new equation:
[tex]4x+48=86[/tex]
In order to get the answer, you need to find the value of x alone, meaning you need to remove everything next to it.
In this equation, 4x is added with 48. That means you need tog et rid of +48 by moving to the other side, which can also be done by adding it with it's opposite. The opposite of +48(positive 48) is -48(negative 48). In order to remove it, subtract 48 from both sides.
[tex]4x+48=86 \rightarrow 4x+48(-48)=86-48 \rightarrow 4x=38[/tex]
Now you're left with 4x=38
Remember that you're trying to find x alone. That means you need to the opposite of what's happening to it.
In this question, x is being multiplied by 4. The opposite of it is dividing by 4.
Divide both sides by 4:
[tex]\frac{4x}{4} =\frac{38}{4} \rightarrow x=9.5[/tex]
The value of Base 2 is 9.5 cm
