What is the area in square centimeters of the triangle pictured here? The triangle has a side named 9cm and 7cm.

Answer 1

To find the area of a triangle, you can use the formula:

\( Area = \dfrac{1}{2} \times Base \times Height \)

In this case, the base of the triangle is the side with a length of 9 cm, and the height (or altitude) can be found by drawing a perpendicular line from the opposite vertex to the base.

Since you are given the other side of the triangle as 7 cm, you can use the Pythagorean theorem to find the height:

\( h = \sqrt{7^2 - 4.5^2} \)
\( h = \sqrt{49 - 20.25} \)
\( h = \sqrt{28.75} \)
\( h \approx 5.36 \, \text{cm} \)

Now you can plug in the values to find the area:

\( Area = \dfrac{1}{2} \times 9 \times 5.36 \)
\( Area = \dfrac{1}{2} \times 48.24 \)
\( Area = 24.12 \, \text{cm}^2 \)

Therefore, the area of the triangle is 24.12 square centimeters.