Method 1:
You can use the formula of an area of equilateral triangle:
[tex]A=\dfrac{a^2\sqrt3}{4}[/tex]
a - length of side
We have a = 10 yd. Substitute:
[tex]A=\dfrac{10^2\sqrt3}{4}=\dfrac{100\sqrt3}{4}=25\sqrt3\ yd^2\\\\\sqrt3\approx1.7\\\\A=25(1.7)=\boxed{42.5\ yd^2}[/tex]
Method 2:
Use the Pythagorean theorem (look at he picture).
[tex]5^2+h^2=10^2[/tex]
[tex]25+h^2=100[/tex] subtract 25 from both sides
[tex]h^2=75\to h=\sqrt{75}\\\\h=\sqrt{25\cdot3}\\\\h=\sqrt{25}\cdot\sqrt3\\\\h=5\sqrt3\ yd[/tex]
The formula of an area of a trinagle:
[tex]A=\dfrac{1}{2}bh[/tex]
b - base
h - height
We have b = 10 yd and h = 5√3 yd. Substitute:
[tex]A=\dfrac{1}{2}(10)(5\sqrt3)=(5)(5\sqrt3)=25\sqrt3\ yd\\\\\sqrt3\approx1.7\\\\A=25(1.7)=\boxed{42.5\ yd^2}[/tex]
