The area of the triangle is:
[tex]\Large\displaystyle\text{$\begin{aligned}A\triangle &= \dfrac{21+7\sqrt{15}}{2}\\ \\A\triangle &\approx 24.055\\ \\\end{aligned}$}[/tex]
You can easily find the area of a triangle using the formula:
[tex]\Large\displaystyle\text{$\begin{aligned}A\triangle = \dfrac{bh}{2}\end{aligned}$}[/tex]
Where h is the height of the triangle, and b the base.
Looking at the figure we can see that h = 7, but we need to discover the base, we know that the base is:
[tex]\Large\displaystyle\text{$\begin{aligned}b = 3 + x\end{aligned}$}[/tex]
Where:
[tex]\Large\displaystyle\text{$\begin{aligned}8^2 &= x^2 + 7^2\\ \\x^2 &= 8^2 - 7^2 \\ \\x^2 &= 64 - 49\\ \\x^2 &= 15\\ \\x &= \sqrt{15}\end{aligned}$}[/tex]
Therefore, our base length is:
[tex]\Large\displaystyle\text{$\begin{aligned}b &= 3 + x\\ \\b &= 3 + \sqrt{15}\\ \\\end{aligned}$}[/tex]
Then we can just apply the formula for the area:
[tex]\Large\displaystyle\text{$\begin{aligned}A\triangle &= \dfrac{(3+\sqrt{15})\cdot 7}{2}\\ \\A\triangle &= \dfrac{21+7\sqrt{15}}{2}\\ \\A\triangle &\approx 24.055\\ \\\end{aligned}$}[/tex]
I hope you liked it
Any doubt? Write it in the comments and I'll help you
