Question

The area of the trapezoid is 48 square meters
Height = ?
bottom = 12 m
Top = 4 m
Right = 10 m
What is the trapezoid's height, H
h= ___ meters

Answer 1

To find the height \( H \) of the trapezoid, we can use the formula for the area of a trapezoid:

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

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

In your case:
- \(\text{Area} = 48 \, \text{m}^2\)
- \( b_1 = 12 \, \text{m} \) (bottom base)
- \( b_2 = 4 \, \text{m} \) (top base)

Substituting these values into the area formula:

\[
48 = \frac{1}{2} \times (12 + 4) \times H
\]

Simplifying the equation:

\[
48 = \frac{1}{2} \times 16 \times H
\]

\[
48 = 8H
\]

Now, solving for \( H \):

\[
H = \frac{48}{8} = 6
\]

Thus, the height \( H \) of the trapezoid is

\[
\boxed{6} \, \text{meters}
\]