What is the height of a trapezoid with an area of 48 square cm and two parallel sides of lengths 8 and 4

To find the height of a trapezoid, we can use the formula for the area of a trapezoid:

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

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

Given:
- \( A = 48 \, \text{cm}^2 \),
- \( b_1 = 8 \, \text{cm} \),
- \( b_2 = 4 \, \text{cm} \).

Now, substitute these values into the formula:

\[
48 = \frac{1}{2} \times (8 + 4) \times h
\]

Simplify the expression:

\[
48 = \frac{1}{2} \times 12 \times h
\]

\[
48 = 6 \times h
\]

Solve for \( h \):

\[
h = \frac{48}{6} = 8 \, \text{cm}
\]

So, the height of the trapezoid is \( 8 \, \text{cm} \).

Would you like more details or have any further questions?

Here are 5 related questions for further exploration:
1. How do you find the height of a triangle if you know its area and base?
2. What happens to the area of a trapezoid if the height is doubled?
3. Can the area formula for a trapezoid be used to find the area of a parallelogram?
4. How do you derive the formula for the area of a trapezoid?
5. How would the height change if the parallel sides were equal in length?

**Tip:** Always double-check units when calculating area or height to avoid confusion with square vs. linear measurements.

What is the height of a trapezoid with an area of 48 square cm and two parallel sides of lengths 8 and 4?

Discover how to calculate the height of a trapezoid with an area of 48 square cm and parallel sides measuring 8 and 4 cm. This solution breaks down the geometry formula for finding the area of a trapezoid and walks through solving for height. Suitable for students in Grades 6-8.

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