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
4 a trapezoid with bases of 6 centimeters and 8 centimeters has an area of 21 square centimeters. what is the height of the trapezoid? draw the trapezoid.
show your work.
solution: ____
5 draw a trapezoid with an area of 17 square centimeters.

Explanation:

Problem 3

Step1: Substitute known values

We know the area formula for a trapezoid is \( A=\frac{1}{2}h(b_1 + b_2) \). Given \( A = 16 \) 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, solve for \( (b_1 + b_2) \) by dividing both sides by 2: \( b_1 + b_2=\frac{16}{2}=8 \) 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 and \( b_2 = 5 \) centimeters (or other pairs like \( 2 \) and \( 6 \), \( 1 \) and \( 7 \), etc.).

Step1: Recall the trapezoid area formula

The formula for the area of a trapezoid is \( A=\frac{1}{2}h(b_1 + b_2) \), where \( A \) is the area, \( h \) is the height, and \( b_1, b_2 \) are the lengths of the two bases.

Step2: Substitute the known values

We know \( A = 21 \) square centimeters, \( b_1 = 6 \) centimeters, and \( b_2 = 8 \) centimeters. Substitute these into the formula:
\( 21=\frac{1}{2}h(6 + 8) \)

Step3: Simplify the equation

First, calculate \( 6 + 8 = 14 \). So the equation becomes \( 21=\frac{1}{2}h\times14 \). Simplify \( \frac{1}{2}\times14 = 7 \), so we have \( 21 = 7h \).

Step4: Solve for \( h \)

Divide both sides of the equation \( 21 = 7h \) by 7: \( h=\frac{21}{7}=3 \) centimeters.

Answer:

(for filling the blanks):
First blank (A): \( 16 \); Second blank (h): \( 4 \); Third blank (A): \( 16 \); Fourth blank (h): \( 4 \); \( (b_1 + b_2) \): \( 8 \); \( b_1 \): \( 3 \) (example); \( b_2 \): \( 5 \) (example)

Problem 4