Question

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.

Explanation:

Step1: Recall trapezoid area formula

The area formula for a trapezoid is \( A=\frac{(b_1 + b_2)}{2}\times h \), where \( b_1 \) and \( b_2 \) are the lengths of the two bases, and \( h \) is the height. We know \( A = 21 \), \( b_1=6 \), \( b_2 = 8 \), and we need to solve for \( h \).

Step2: Substitute known values into the formula

Substitute \( A = 21 \), \( b_1 = 6 \), \( b_2=8 \) into the formula: \( 21=\frac{(6 + 8)}{2}\times h \). First, calculate the sum of the bases: \( 6+8 = 14 \). Then the formula becomes \( 21=\frac{14}{2}\times h \), and \( \frac{14}{2}=7 \), so \( 21 = 7h \).

Step3: Solve for \( h \)

To find \( h \), divide both sides of the equation \( 21 = 7h \) by 7: \( h=\frac{21}{7}=3 \).

Answer:

The height of the trapezoid is 3 centimeters.