Question

The Area of the trapezoid is 9 square centimeters
Height = ?
Bottom = 4 cm
Top = 2 cm
Left = 4 cm
What is the Trapezoids height h
h = ______ centimeters

Answer 1

The area \( A \) of a trapezoid can be calculated using the formula:

\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\]

where \( b_1 \) and \( b_2 \) are the lengths of the two bases (the top and bottom), and \( h \) is the height.

In this case:
- \( A = 9 \) square centimeters
- \( b_1 = 4 \) cm (bottom base)
- \( b_2 = 2 \) cm (top base)

Substituting the known values into the formula:

\[
9 = \frac{1}{2} \times (4 + 2) \times h
\]

This simplifies to:

\[
9 = \frac{1}{2} \times 6 \times h
\]

\[
9 = 3h
\]

Now, solve for \( h \):

\[
h = \frac{9}{3} = 3
\]

Thus, the height \( h \) of the trapezoid is:

\[
h = 3 \text{ centimeters}
\]