a trapezoid abcd has the bases length of a is equal to 120 mm and c 86 mm and the area a is equal to 2575 mm squared. find the height of the trapezoid

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

\[
A = \frac{1}{2} \cdot (a + b) \cdot h
\]

Where:
- \( A \) is the area,
- \( a \) and \( b \) are the lengths of the two parallel sides (bases),
- \( h \) is the height.

In this case:
- \( A = 2575 \, \text{mm}^2 \),
- \( a = 120 \, \text{mm} \),
- \( b = 86 \, \text{mm} \),
- \( h \) is the unknown.

Let's plug the known values into the formula and solve for \( h \):

\[
2575 = \frac{1}{2} \cdot (120 + 86) \cdot h
\]

\[
2575 = \frac{1}{2} \cdot 206 \cdot h
\]

\[
2575 = 103 \cdot h
\]

Now, solve for \( h \):

\[
h = \frac{2575}{103}
\]

Let me calculate the value of \( h \).The height \( h \) of the trapezoid is \( 25 \, \text{mm} \).

Would you like more details or have any questions? Here are some related questions for further exploration:

1. How do you calculate the perimeter of a trapezoid?
2. What is the difference between an isosceles trapezoid and a general trapezoid?
3. How does the area formula change for other quadrilaterals like parallelograms?
4. Can you solve for the height of a trapezoid if the area is not directly given?
5. How can you find the angles of a trapezoid if only the sides are known?

**Tip:** The trapezoid's height can also be derived geometrically, using Pythagoras' theorem, if diagonal lengths are provided.

A trapezoid ABCD has the bases length of a = 120 mm and c = 86 mm, and the area A = 2575 mm². Find the height of the trapezoid.

Learn how to calculate the height of a trapezoid with base lengths of 120 mm and 86 mm, and an area of 2575 mm². This solution covers essential geometry concepts, including the trapezoid area formula and step-by-step instructions for solving linear equations. Suitable for students in Grades 6-8.

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