Answer:
[tex]\large\boxed{A=\dfrac{3\sqrt{187}}{4}\ cm^2\approx10.26\ cm^2}[/tex]
Step-by-step explanation:
It's the isosceles triangle (look at the picture).
The formula of an area of a triangle:
[tex]A=\dfrac{bh}{2}[/tex]
b - base
h - height
Use the Pythagorean theorem to calculate the height:
[tex]1.5^2+h^2=7^2\\\\2.25+h^2=49\qquad\text{subtract 2.25 from both sides}\\\\h^2=46.75\to h=\sqrt{46.75}\\\\h=\sqrt{\dfrac{4675}{100}}\\\\h=\dfrac{\sqrt{4675}}{\sqrt{100}}\\\\h=\dfrac{\sqrt{25\cdot187}}{10}\\\\h=\dfrac{\sqrt{25}\cdot\sqrt{187}}{10}\\\\h=\dfrac{5\sqrt{187}}{10}\\\\h=\dfrac{\sqrt{187}}{2}\ cm[/tex]
We have:
[tex]b=3cm,\ h=\dfrac{\sqrt{187}}{2}\ cm[/tex]
Substitute:
[tex]A=\dfrac{3\cdot\frac{\sqrt{187}}{2}}{2}=\dfrac{3\sqrt{187}}{4}\ cm^2[/tex]
