Question

solve.
3 draw a trapezoid with a height of 4 centimeters and an area of 16 square centimeters.
$a = \frac{1}{2}h(b_1 + b_2)$
__ $= \frac{1}{2} \times$ __ $\times (b_1 + b_2)$
since __ $= \frac{1}{2} \times$ $\times 8, (b_1 + b_2) =$ __.
choose: $b_1 =$ ____ centimeters
$b_2 =$ ____ centimeters

Explanation:

Step1: Recall trapezoid area formula

The area formula for a trapezoid is \( A=\frac{1}{2}h(b_1 + b_2) \), where \( A \) is the area, \( h \) is the height, \( b_1 \) and \( b_2 \) are the lengths of the two bases. We know \( A = 16 \) square centimeters and \( h=4 \) centimeters. Substitute these values into the formula: \( 16=\frac{1}{2}\times4\times(b_1 + b_2) \)

Step2: Simplify the equation

First, calculate \( \frac{1}{2}\times4 = 2 \), so the equation becomes \( 16 = 2\times(b_1 + b_2) \). Then, divide both sides by 2: \( \frac{16}{2}=b_1 + b_2 \), so \( b_1 + b_2 = 8 \) centimeters.

Step3: Choose values for \( b_1 \) and \( b_2 \)

We can choose any two positive numbers that add up to 8. For example, let \( b_1 = 3 \) centimeters, then \( b_2=8 - 3 = 5 \) centimeters (or other pairs like \( b_1 = 2 \), \( b_2 = 6 \); \( b_1 = 4 \), \( b_2 = 4 \) etc.)

Filling in the blanks:
First blank (A): \( 16 \)
Second blank (h): \( 4 \)
Third blank (left side of equation after substitution): \( 16 \)
Fourth blank (h): \( 4 \)
Fifth blank (result of \( b_1 + b_2 \)): \( 8 \)
For \( b_1 \) and \( b_2 \), we can choose \( b_1 = 3 \), \( b_2 = 5 \) (or other valid pairs)

Answer:

Filling the blanks (example with \( b_1 = 3 \), \( b_2 = 5 \)):
\( 16=\frac{1}{2}\times4\times(b_1 + b_2) \)
Since \( 16=\frac{1}{2}\times4\times(b_1 + b_2) \), \( (b_1 + b_2)=8 \).
Choose: \( b_1 = 3 \) centimeters, \( b_2 = 5 \) centimeters (other valid pairs like \( b_1 = 2, b_2 = 6 \); \( b_1 = 4, b_2 = 4 \) are also acceptable)