To find the simplified expression that represents the area of the triangle, we will follow these steps:
1. Identify the formula:
The formula for the area [tex]\(A\)[/tex] of a triangle is given by:
[tex]\[
A = \frac{1}{2} \cdot b \cdot h
\][/tex]
where [tex]\(b\)[/tex] is the base and [tex]\(h\)[/tex] is the height.
2. Substitute the given values:
In this problem, the values given are:
[tex]\[
b = 10 \, \text{cm}
\][/tex]
[tex]\[
h = 5 \, \text{cm}
\][/tex]
3. Plug these values into the formula:
We substitute [tex]\(b = 10 \, \text{cm}\)[/tex] and [tex]\(h = 5 \, \text{cm}\)[/tex] into the formula:
[tex]\[
A = \frac{1}{2} \cdot 10 \, \text{cm} \cdot 5 \, \text{cm}
\][/tex]
4. Simplify the expression:
First, we multiply the base and the height:
[tex]\[
10 \, \text{cm} \cdot 5 \, \text{cm} = 50 \, \text{cm}^2
\][/tex]
Then, we multiply by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2} \cdot 50 \, \text{cm}^2 = 25 \, \text{cm}^2
\][/tex]
Hence, the simplified expression that represents the area of this triangle is:
[tex]\[
25 \, \text{cm}^2
\][/tex]
