https://file.aiquickdraw.com/mathbot/file/1729085680262nx0lcjka.jpg

The image shows a triangle with three sides labeled: 12.5 cm, 7.8 cm, and 6.9 cm. There is also a right-angle indicator with a perpendicular height of 4.2 cm.

To find the area of this triangle, we can use the formula for the area of a triangle:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

In this case, the base is given as 7.8 cm, and the height is 4.2 cm (the perpendicular distance).

\[
\text{Area} = \frac{1}{2} \times 7.8 \, \text{cm} \times 4.2 \, \text{cm}
\]

\[
\text{Area} = \frac{1}{2} \times 32.76 \, \text{cm}^2
\]

\[
\text{Area} = 16.38 \, \text{cm}^2
\]

So, the area of the triangle is **16.38 cm²**.

Do you need further explanation or details? 

Here are five related questions to think about:
1. How would the area change if the base was doubled but the height stayed the same?
2. What if the height was halved but the base stayed the same?
3. How could you find the area of the triangle if only the three side lengths were given?
4. What is the significance of the perpendicular height in calculating the area of triangles?
5. Could you use trigonometric methods to find the area if only angles and sides were provided?

**Tip:** For triangles where the height is not directly given, methods like Heron's formula or trigonometric area formulas can be helpful!

Find the area of the triangle with a base of 7.8 cm, height of 4.2 cm, and other side lengths of 6.9 cm and 12.5 cm.

Learn how to calculate the area of a triangle with base 7.8 cm and height 4.2 cm. This geometry problem covers the area of triangles using the formula A = 1/2 * base * height, suitable for students in Grades 6-8.

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