Question

The area of a given trapezoid is 86cm. Base 1 is 12cm and the height is 8cm. What is the length of Base 2. The formula for a trapezoid is A=1/2(b1+b2)h

Answer 1

Here is the formula:

`A=(1)/(2)(b1+b2)h`

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.

• Base 1 ⇒ b1

• Height ⇒ h

• Area ⇒ A

Replace the variables used in the formula with the values you are given.

`A=(1)/(2)(b1+b2)h \\ \\ 86=(1)/(2)(12+b2)8`

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.

`86=(1)/(2)(12+b2)8 \rightarrow 86=((1)/(2)(12+x))(8)`

Multiply everything in the parentheses, but first start with the first one(parenthesis).

`86=((1)/(2)(12+x))(8) \rightarrow 86= (6+0.5x)(8)`

You need to have only 1 number/variable on each side. That means you have to multiply the values in the two parentheses:

`(6+0.5x)(8) \rightarrow 4x+48`

Here is your new equation:

`4x+48=86`

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.

`4x+48=86 \rightarrow 4x+48(-48)=86-48 \rightarrow 4x=38`

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:

`(4x)/(4) =(38)/(4)  \rightarrow x=9.5`

The value of Base 2 is 9.5 cm