Question

If the area of this trapezoid is A=57 then what must is height h be
Height = ?
Top = 7
Bottom = 12
is the answer
h=3
h=6
h=6.5
h=19

Answer 1

To find the height \( h \) of the trapezoid with the given area \( A = 57 \), we can use the formula for the area of a trapezoid:

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

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

In this case:
- \( b_1 \) (top) = 7
- \( b_2 \) (bottom) = 12

Substituting the values into the area formula:

\[
57 = \frac{1}{2} \times (7 + 12) \times h
\]

Calculating the sum of the bases:

\[
7 + 12 = 19
\]

Now, substitute this back into the area formula:

\[
57 = \frac{1}{2} \times 19 \times h
\]

Multiply both sides by 2 to eliminate the fraction:

\[
114 = 19 \times h
\]

Now, solve for \( h \):

\[
h = \frac{114}{19}
\]

Calculate \( h \):

\[
h = 6
\]

So, the height \( h \) of the trapezoid is \( 6 \).

Therefore, the answer is **h = 6**.