To solve for [tex]\(a\)[/tex] from the given equation [tex]\(A=\frac{a+b}{2} \cdot h\)[/tex], proceed with the following steps:
1. Start with the given equation:
[tex]\[
A = \frac{a+b}{2} \cdot h
\][/tex]
2. Isolate the fraction that involves [tex]\(a\)[/tex]:
[tex]\[
A = \frac{h(a + b)}{2}
\][/tex]
3. Remove the fraction by multiplying both sides by 2:
[tex]\[
2A = h(a + b)
\][/tex]
4. Isolate the term involving [tex]\(a\)[/tex] by dividing both sides by [tex]\(h\)[/tex]:
[tex]\[
\frac{2A}{h} = a + b
\][/tex]
5. Solve for [tex]\(a\)[/tex] by subtracting [tex]\(b\)[/tex] from both sides:
[tex]\[
a = \frac{2A}{h} - b
\][/tex]
Therefore, the solution for [tex]\(a\)[/tex] is:
[tex]\[
a = \frac{A}{h} - \frac{b}{2}
\][/tex]
This is the required expression for [tex]\(a\)[/tex].
