Question

The formula for the area of a trapezoid is $A = \dfrac{1}{2}({b_1} + {b_2})h$ . How do you solve for $b{}_1$ ?

Answer 1

Hint: For solving this particular question for $b{}_1$ where formula for the surface area of a trapezoid is given as $A = \dfrac{1}{2}({b_1} + {b_2})h$ , you have to isolate $b{}_1$ terms while keeping the equation balanced.

Complete step by step answer:
Understanding the trapezoid with following figure,

It is given that the formula for area of the trapezoid is $A = \dfrac{1}{2}({b_1} + {b_2})h$.
And we have to solve for $b{}_1$ .
Let us take ,
$A = \dfrac{1}{2}({b_1} + {b_2})h$
Now, multiply by two on both sides. We will get ,
$
   \Rightarrow 2 \times A = 2 \times \dfrac{1}{2}({b_1} + {b_2})h \\
   \Rightarrow A = ({b_1} + {b_2})h \\
 $
Now, divide by $h$ both sides. We will get,
$
   \Rightarrow \dfrac{A}{h} = \dfrac{{({b_1} + {b_2})h}}{h} \\
   \Rightarrow \dfrac{A}{h} = ({b_1} + {b_2}) \\
 $
Now, subtract ${b_2}$ from both sides. We will get ,
\[
   \Rightarrow \dfrac{A}{h} - {b_2} = ({b_1} + {b_2}) - {b_2} \\
   \Rightarrow \dfrac{A}{h} - {b_2} = {b_1} \\
 \]
We can write this as,
\[ \Rightarrow {b_1} = \dfrac{A}{h} - {b_2}\]

Additional Information:
A trapezoid, also said as a trapezium, may be a quadrilateral with one pair of parallel sides and another pair of non-parallel sides. Like square and rectangle, trapezoid is additionally flat.
In a trapezoid, the pair of parallel sides are referred to as the bases while the pair of non-parallel sides are referred to as the legs. The perpendicular distance between the two parallel sides of a trapezium is thought to be the height of a trapezoid.
In simple words, the bottom and height of a trapezoid are perpendicular to every other.

Note: The solution of the addition or subtraction between two numbers will have the sign of the greater number. If the two numbers have different signs like positive and negative then subtract the two numbers and provide the sign of the larger number. If the two numbers have the same sign i.e., either positive or negative signs then add the two numbers and provide the common sign.