The bases of a trapezoid are 8 centimeters and 12 centimeters, and the height is h centimeters. Which equation can be used to represent A, the area of the trapezoid in square centimeters?

The formula for the area \( A \) of a trapezoid is:

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

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

For your trapezoid:
- \( b_1 = 8 \) cm,
- \( b_2 = 12 \) cm.

Substitute these values into the formula:

\[
A = \frac{1}{2} \times (8 + 12) \times h
\]

Simplify the equation:

\[
A = \frac{1}{2} \times 20 \times h
\]

\[
A = 10h
\]

Thus, the equation representing the area \( A \) in terms of the height \( h \) is:

\[
A = 10h
\]

Would you like more details or have any questions?

Here are 5 related questions you might find helpful:
1. How do we derive the formula for the area of a trapezoid?
2. What if the height \( h \) was given as 5 cm? What would be the area?
3. How would the area change if one of the bases was doubled?
4. Can the area of a trapezoid be negative?
5. How does the area formula for a trapezoid compare with that of a parallelogram?

**Tip:** Remember, the height of a trapezoid is always the perpendicular distance between the two parallel bases.

Learn how to find the area of a trapezoid with bases of 8 cm and 12 cm, and height h. This detailed explanation covers the key formula A = 1/2 × (b1 + b2) × h, simplified to A = 10h, ideal for students in Grades 6-8.

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