 A trapezoid has a height of 8xy centimeters.  Its shorter base is 19y centimeters, and its longer base is 23y centimeters.  Use the given formula to find the area of the trapezoid.
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The formula to find the area \( A \) of a trapezoid is given by:

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

Where:
- \( b_1 \) is the length of the shorter base,
- \( b_2 \) is the length of the longer base,
- \( h \) is the height of the trapezoid.

We are given the following values:
- \( b_1 = 19y \) cm,
- \( b_2 = 23y \) cm,
- \( h = 8xy \) cm.

Now, substitute these values into the formula:

\[
A = \frac{1}{2} \times (19y + 23y) \times 8xy
\]

Simplify the expression:

\[
A = \frac{1}{2} \times 42y \times 8xy
\]

\[
A = \frac{1}{2} \times 336xy^2
\]

\[
A = 168xy^2 \, \text{square centimeters}.
\]

Thus, the area of the trapezoid is \( \boxed{168xy^2} \, \text{square centimeters} \).

Would you like further details or explanations? Here are some additional questions for practice:

1. How does the formula for the area of a trapezoid differ from that of a rectangle?
2. What happens to the area if the height of the trapezoid is doubled?
3. If the shorter base were 21y cm instead of 19y cm, how would the area change?
4. Can you derive the formula for the area of a trapezoid from basic geometric principles?
5. What if the height was given as \( h = 8x^2y \) instead of \( 8xy \)? How would the area be calculated?

**Tip**: When working with geometric formulas, always make sure that all units are consistent throughout your calculations!

A trapezoid has a height of 8xy centimeters. Its shorter base is 19y centimeters, and its longer base is 23y centimeters. Use the given formula to find the area of the trapezoid.

This page provides a step-by-step solution to finding the area of a trapezoid with a height of 8xy cm, a shorter base of 19y cm, and a longer base of 23y cm. Learn how to apply the formula for the area of a trapezoid, suitable for students in Grades 8-10.

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